𝗧𝗜𝗠𝗘𝗦𝗧𝗔𝗠𝗣𝗦 *🚬(´ε｀ )* 00:36 *Nature of Chapter* 02:01 Weightage 02:20 *📍Index* 03:07 *🔥Critical Topics* 04:42 *Second Fundamental Theorem of Calculus* 06:58 _🚬 Be careful of mod and √(x²) expressions_ 08:42 _🚬 Use of Substitution_ 11:05 _🚬 Indeterminate Form after putting Limits_ 14:02 _🚬 Use of By Parts_ 24:11 *”* 20:01 _🚬 d{f(x)} given instead of dx_ 22:47 *⚡REMARK:* Substitution must be continuous in the interval of integration 26:52 _🚬 Relating Integrals ✨_ 32:56 *⚡RESULT:* When Integrand is Discontinuous in the interval of integration 38:04 _🚬 Breaking Limits for G.I.F (METHOD⚡)_ 42:38 _Toughest Question_ 49:54 🚬 Derivative inside Integration 55:53 *Geometrical Interpretation of Definite Integrals* 1:04:46 *⚡REMARK* 1:06:26 *Properties of Definite Integration* 1:07:44 *Property ①②③* 1:21:42 *⚡ REMARK:* Integration involving inverse functions 1:28:21 *Property ④:* King’s Rule 1:29:09 ➙1ˢᵗ Use: For Removing unwanted 𝑥 from Integrand 1:39:38 ➙2ⁿᵈ Use: Terms Flip 1:54:00 *💡Tip:* When Integrand has exponential func & a+b=0, use King Rule 2:00:15 _Good Question of F.P.F_ 2:07:37 *Property ⑤* *General Form* ➙ ₋ₐ∫ᵃ f(x) dx = ₀∫ᵃ f(x) + f(-x) dx 2:11:17 *Property ⑥:* Queen’s Rule 2:12:58 When to use 🂮 & when 🂽 2:20:32 *🧠 REMEMBER* 2:28:00 *Observations for Manipulating Limits* 2:28:37 Trick to Remember 🌟 2:32:26 _🚬 If 2 or more Integrals in addition/substraction given, try to make their limits same_ 2:40:09 *Integration of Periodic Function* 2:48:54 _Function Equation concept to find Period_ 2:54:13 *⚡NOTE:* Integral of even func is odd & vice-versa 2:55:16 *Bounds of Definite Integrals (Estimation)* 2:55:47 Property ① & ② 2:58:30 Property ③ 2:58:45 Property ④ 3:02:35 _🚬 Method to find Bounds_ 3:08:22 _🚬 Taylor Expansions used_ 3:12:38 _🚬 When sq. root comes_ 3:14:35 *Equations in Definite Integrals* *(Use of Leibnitz)* 3:22:11 _🚬 When differentiating doesn't work_ 3:29:16 *Reduction Formulae* 3:36:55 *Walli’s Formula* 3:41:26 *Summation of Infinite Series using Definite Integral* 3:42:31 *Formula* 3:50:08 _🚬 Product given instead of Summation_ 3:59:20 _Question where Formula don't suffice_ 4:03:10 *Derivation & Upper/Lower Reimann Sum*
IMP Q Q1 Good quest, IMP Concept 21:04 Q2 V Good Q 27:56 Q3 OP Question could not solve 43:10 Q4 Good quest 46:34 Q5 Good ques 50:45 Q6 OP Question 1:01:15 Q7 Good Question 1:09:35
5:0612:4851:53 : General version of 2nd Fundamental (limits) 9:189:38 : Jiske (variable) respect mein integrate kr rhe, usi ke limits lagaenge 20:4121:32 : 23:36 : Jisko =t put kr rhe (substitution), usko interval of integration mein continuous hona chahiye 26:58 : Ratio of 2 integrals is asked (⚠️ : Don't solve both integrals) ➡️ 27:52 : Create the other integral from one integral (using by parts with "1") ➡️ 30:053:32:13 : By parts mein spl technique : Jab bhi I bnane ka mauka mile, bina hesitation ke bnado. 2:21:52 1:22:40 1:23:58 1:26:26 1:27:50 : Integral mein f-¹ :- Put f-¹(x) = t. ➡️ dx=f'(t) [as x=f(t)] ➡️ Apply By Parts
KING'S RULE Use 1 : To remove unwanted x 1:29:32 1:30:00 1:35:42 2:16:22 1:31:22 1:32:33 1:36:00 1:46:14 1:53:26 1:55:46 2:02:05 2:06:34 : King's Rule lagane ka asli impact addition (of the integrals) par aata h Use 2 : Terms are Symm. / Cyclic after applying King's Rule 1:39:43 1:40:59 1:41:24 Toh add krne par terms kat jaengi. 🌟🌟🌟 ( 1:40:36 1:41:51 1:45:50 2:01:34 2:01:44 2:03:49 2:05:39 ) 1:32:53 1:33:30 : f(x) pta nhi hona is a good sign. Matlab integration toh Krna hi nhi h (f nhi pta toh integrate kr hi nhi skte). 1:33:13 ( 🌟 )Isko property apply krke kisi aur form mein express Krna h General form of Kings Rule : - 1:49:36 1:49:48 1:52:29 (🌟) 1:53:48 : Yaha bas a+b (angle) accha hoga just like oopar 'a' accha tha. Baki sab same h 1:50:10 (Use 1 : Remove unwanted x) 1:51:31 (Use 2 : Cyclic terms ; (a+b) angle is good) 1:51:56 1:52:58 (Use 2 : Cyclic terms ; (a+b) number is good) 1:54:47 1:57:13 : exponential baitha h integral mein ; (a+b) = 0 ➡️ Apply Kings Rule ( & add) ➡️ Exponential wali term kat jaegi 2:04:26 🌟🌟 : Q mein jyada kuch smjh nhi aa rha, std cheezein not working ; check for term jiska standard substitution humein aata h. Agar aesa term h, toh use standard substitution. 2:04:44
QUEEN'S RULE 2:13:30 2:14:03 2:14:28 2:17:49 2:18:35 : King vs Queen Rule : If f(UL - x) = f(x) or -f(x) ➡️ Queens Rule. Otherwise King's Rule 2:19:34 2:21:03 2:24:22 : Queen lgane par lmt half ho jati h 2:26:00 2:26:28 : Interpreting the Q. 2:26:44 : Definite se Krna h. 🌟🌟 Lmt 0 se 'a' dikhi ➡️ Without a sec, check f(UL - x). 2:27:24 : 0 se 'a' lmt dikhi toh King / Queen ka sochna hi h. No two ways about it.
Limit Manipulation : Limit x (variable) ki hoti h 2:29:01 2:29:46 . Toh jo limit ke saath Krna chahte ho, whi x ke saath krke = t put krdo. 2:29:35 2:30:30 2:32:26 2:39:22 2:36:22 ( 2:36:32 ) : Jab bhi Integrals in addition/ subtraction ➡️ Make limits of the integrals same jisse poora ek integral bn jaye and terms kat pit jayein aur expression simplify ho jaye. 2:35:55
Periodic function 2:40:54 2:41:18 2:41:47 2:42:45 2:51:24 2:51:34 : Koi bhi T length ke interval ka integral same hota h 2:50:44 : Functional eqn mein T dekhna... BOUNDS 3:02:57 3:03:54 3:06:12 : 3:08:26 : Bound ke Q mein expansion bhi expect kr skte hn...🌟 3:12:43 3:13:55 : Bound ka Q. ; Integral mein Sq. root wale terms hn... Eqns In Definite Integrations 3:15:32 3:17:11 3:17:35 : Just Differentiate. Easy Q. Mein differentiate krte hi answer aa jaega 3:18:55 3:21:41 : In a better Q., after Differentiation, a Differential Eqn will be formed in f(x) & f'(x). Solve that DE to obtain f(x) 3:24:44 : ⚠️ 3:22:31 : ⚠️ (Variable of integration dekho. Jo bhi alag variable wale terms h unhein integral se bhara kro)
good evening, sir, as u said if we can ignore a single point during definite integration then why cannot we ignore the point at which the function is discontinuous
Bound waala sawaal Done and Dusted 😍really is wale question se bohut badhiya understanding milli, and found that this question is really easy, if you are used to function expansions
Yahan dx se multiply divide is same as writing d(sinx) as cosxdx.... Moment you made it integral wrt dx, limits will change as pr x kahan se kahan vary kr rha hai... Best wishes❤❤❤
Sir, I have a doubt please clear kar dijiye...mere 12th me less than 75% aaye the aur kisi reason ki vjh se jee preparation drop year me start ki ( yaani isi year ) vo bhi late me. to nios se 12th repeat kr rha hu to ky mai ab second drop lu to nios board ke according jee advance 2026 me de skta hu..?abhi ek baar bhi advance nhi diya h.
advance sirf 2 baar de sakte hai :- with 12th class & just next year {tumne agar 12th ke sath advance NHI diya , then you are left with ONLY 1 attempt that too just next year , 2nd drop advance mai allowed NHI hai }
@@IITD-or6fw but mai 12th repeat kr rhaa hu with nios board, aur abhi ek baar bhi exam nhi diya h na to jee mains na advanced. To agr maine ek baar bhi exam nhi diya to aur mai 12th repeat kr rha hu to kaise pta chlega ki I am a dropper
The PDF of the session Definite Integration is in the link:- unacademy.com/content/jee/unacademy-nexus-jee-play
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Yes download kese Kiya bhai
𝗧𝗜𝗠𝗘𝗦𝗧𝗔𝗠𝗣𝗦 *🚬(´ε｀ )*
00:36 *Nature of Chapter*
02:01 Weightage
02:20 *📍Index*
03:07 *🔥Critical Topics*
04:42 *Second Fundamental Theorem of Calculus*
06:58 _🚬 Be careful of mod and √(x²) expressions_
08:42 _🚬 Use of Substitution_
11:05 _🚬 Indeterminate Form after putting Limits_
14:02 _🚬 Use of By Parts_
24:11 *”*
20:01 _🚬 d{f(x)} given instead of dx_
22:47 *⚡REMARK:* Substitution must be continuous in the interval of integration
26:52 _🚬 Relating Integrals ✨_
32:56 *⚡RESULT:* When Integrand is Discontinuous in the interval of integration
38:04 _🚬 Breaking Limits for G.I.F (METHOD⚡)_
42:38 _Toughest Question_
49:54 🚬 Derivative inside Integration
55:53 *Geometrical Interpretation of Definite Integrals*
1:04:46 *⚡REMARK*
1:06:26 *Properties of Definite Integration*
1:07:44 *Property ①②③*
1:21:42 *⚡ REMARK:* Integration involving inverse functions
1:28:21 *Property ④:* King’s Rule
1:29:09 ➙1ˢᵗ Use: For Removing unwanted 𝑥 from Integrand
1:39:38 ➙2ⁿᵈ Use: Terms Flip
1:54:00 *💡Tip:* When Integrand has exponential func & a+b=0, use King Rule
2:00:15 _Good Question of F.P.F_
2:07:37 *Property ⑤*
*General Form* ➙ ₋ₐ∫ᵃ f(x) dx = ₀∫ᵃ f(x) + f(-x) dx
2:11:17 *Property ⑥:* Queen’s Rule
2:12:58 When to use 🂮 & when 🂽
2:20:32 *🧠 REMEMBER*
2:28:00 *Observations for Manipulating Limits*
2:28:37 Trick to Remember 🌟
2:32:26 _🚬 If 2 or more Integrals in addition/substraction given, try to make their limits same_
2:40:09 *Integration of Periodic Function*
2:48:54 _Function Equation concept to find Period_
2:54:13 *⚡NOTE:* Integral of even func is odd & vice-versa
2:55:16 *Bounds of Definite Integrals (Estimation)*
2:55:47 Property ① & ②
2:58:30 Property ③
2:58:45 Property ④
3:02:35 _🚬 Method to find Bounds_
3:08:22 _🚬 Taylor Expansions used_
3:12:38 _🚬 When sq. root comes_
3:14:35 *Equations in Definite Integrals*
*(Use of Leibnitz)*
3:22:11 _🚬 When differentiating doesn't work_
3:29:16 *Reduction Formulae*
3:36:55 *Walli’s Formula*
3:41:26 *Summation of Infinite Series using Definite Integral*
3:42:31 *Formula*
3:50:08 _🚬 Product given instead of Summation_
3:59:20 _Question where Formula don't suffice_
4:03:10 *Derivation & Upper/Lower Reimann Sum*
Broo
The best maths teacher ever existed ❤️❤️
Sso true
Aavo kabhi Ashish Agarwal sir ki haweli prr guru ❤🎉
racoon like fingers dekh ke behta h kya
@@PragyanSrivastava_JEEaspirant. aao kbhi GB sir ke tower pe
@@PragyanSrivastava_JEEaspirant. sir bhi ache hai but arvind sir tarun sir and sachin sir are love
IMP Q
Q1 Good quest, IMP Concept 21:04
Q2 V Good Q 27:56
Q3 OP Question could not solve 43:10
Q4 Good quest 46:34
Q5 Good ques 50:45
Q6 OP Question 1:01:15
Q7 Good Question 1:09:35
5:06 12:48 51:53 : General version of 2nd Fundamental (limits)
9:18 9:38 : Jiske (variable) respect mein integrate kr rhe, usi ke limits lagaenge
20:41 21:32 :
23:36 : Jisko =t put kr rhe (substitution), usko interval of integration mein continuous hona chahiye
26:58 : Ratio of 2 integrals is asked (⚠️ : Don't solve both integrals) ➡️ 27:52 : Create the other integral from one integral (using by parts with "1") ➡️ 30:05 3:32:13 : By parts mein spl technique : Jab bhi I bnane ka mauka mile, bina hesitation ke bnado. 2:21:52
1:22:40 1:23:58 1:26:26 1:27:50 : Integral mein f-¹ :-
Put f-¹(x) = t. ➡️ dx=f'(t) [as x=f(t)] ➡️ Apply By Parts
KING'S RULE
Use 1 : To remove unwanted x 1:29:32 1:30:00 1:35:42 2:16:22
1:31:22 1:32:33 1:36:00 1:46:14 1:53:26 1:55:46 2:02:05 2:06:34 : King's Rule lagane ka asli impact addition (of the integrals) par aata h
Use 2 : Terms are Symm. / Cyclic after applying King's Rule 1:39:43 1:40:59 1:41:24
Toh add krne par terms kat jaengi.
🌟🌟🌟 ( 1:40:36 1:41:51 1:45:50 2:01:34 2:01:44 2:03:49 2:05:39 )
1:32:53 1:33:30 : f(x) pta nhi hona is a good sign. Matlab integration toh Krna hi nhi h (f nhi pta toh integrate kr hi nhi skte). 1:33:13 ( 🌟 )Isko property apply krke kisi aur form mein express Krna h
General form of Kings Rule : -
1:49:36 1:49:48 1:52:29 (🌟) 1:53:48 : Yaha bas a+b (angle) accha hoga just like oopar 'a' accha tha. Baki sab same h
1:50:10 (Use 1 : Remove unwanted x)
1:51:31 (Use 2 : Cyclic terms ; (a+b) angle is good)
1:51:56 1:52:58 (Use 2 : Cyclic terms ; (a+b) number is good)
1:54:47 1:57:13 : exponential baitha h integral mein ; (a+b) = 0 ➡️ Apply Kings Rule ( & add) ➡️ Exponential wali term kat jaegi
2:04:26 🌟🌟 : Q mein jyada kuch smjh nhi aa rha, std cheezein not working ; check for term jiska standard substitution humein aata h. Agar aesa term h, toh use standard substitution. 2:04:44
QUEEN'S RULE
2:13:30 2:14:03 2:14:28 2:17:49 2:18:35 : King vs Queen Rule : If f(UL - x) = f(x) or -f(x) ➡️ Queens Rule. Otherwise King's Rule 2:19:34 2:21:03
2:24:22 : Queen lgane par lmt half ho jati h
2:26:00 2:26:28 : Interpreting the Q.
2:26:44 : Definite se Krna h. 🌟🌟 Lmt 0 se 'a' dikhi ➡️ Without a sec, check f(UL - x).
2:27:24 : 0 se 'a' lmt dikhi toh King / Queen ka sochna hi h. No two ways about it.
Limit Manipulation : Limit x (variable) ki hoti h 2:29:01 2:29:46 . Toh jo limit ke saath Krna chahte ho, whi x ke saath krke = t put krdo. 2:29:35 2:30:30
2:32:26 2:39:22 2:36:22 ( 2:36:32 ) : Jab bhi Integrals in addition/ subtraction ➡️ Make limits of the integrals same jisse poora ek integral bn jaye and terms kat pit jayein aur expression simplify ho jaye. 2:35:55
Periodic function
2:40:54 2:41:18 2:41:47 2:42:45 2:51:24 2:51:34 : Koi bhi T length ke interval ka integral same hota h
2:50:44 : Functional eqn mein T dekhna...
BOUNDS
3:02:57 3:03:54 3:06:12 :
3:08:26 : Bound ke Q mein expansion bhi expect kr skte hn...🌟
3:12:43 3:13:55 : Bound ka Q. ; Integral mein Sq. root wale terms hn...
Eqns In Definite Integrations
3:15:32 3:17:11 3:17:35 : Just Differentiate. Easy Q. Mein differentiate krte hi answer aa jaega
3:18:55 3:21:41 : In a better Q., after Differentiation, a Differential Eqn will be formed in f(x) & f'(x). Solve that DE to obtain f(x)
3:24:44 : ⚠️
3:22:31 : ⚠️ (Variable of integration dekho. Jo bhi alag variable wale terms h unhein integral se bhara kro)
3:34:51 3:36:01 :
4:15:41 🌟🌟🌟
good evening, sir, as u said if we can ignore a single point during definite integration then why cannot we ignore the point at which the function is discontinuous
3:12:03 sir doubt hai xcosx> 3/8 hoga na ki equal option me equal diya hai ,then what to do
Why you play a very critical role in all over jee preparation want to meet you after selection❤❤❤
The last questions was so much fun!! absolutely mind blowing!
Limit same banane wala sawal done and dusted ✓✓
2:39:16
Love you Sir ❤️ maja aa gya
59:31 wala sawal king's rule se kar diya 💀🗿
2:39:04 answer = 0 limit same banane wala sawal done and dusted
36:56 pe open hoga ya close open hoga sir?
1hr vale 5400 2hr vale 0045, 0335,0740,1125,2030,2540,2808,4010,5411
3:28:47 imp concept
21:30
27:40
52:00
1:01:30
Bound waala sawaal Done and Dusted 😍really is wale question se bohut badhiya understanding milli, and found that this question is really easy, if you are used to function expansions
3:02:04 see prove Karen ke liye increasing fxn hon a chai ye na 😅
Wonderful session sir .. learnt so many things🫶
bhai aapse achi maths koi nahi padhata ❤❤❤
mara bhai sara sawal done and dusted.
When I see you sir then I am very happy
Sir you're very session really helped me thank you sir you're the best ❤
3:04:58 CONTINUING TOMARROW❤😊😊
finished ?
bhai yeh chapter pehli baar krrha hu kya ye lecture dekhlu?
Yeah
sir in qus no.1 integral of cosx is sinx but you've changed the sign.....if anyone know this then please help me
2nd question integration of sinx will be done
Limit same banane wla done and dusted
lol
1:12:27 sir ne galat likhdiya
Full class 12th for board exam ek lecture bana dijiye na sir please 😊😊😊😊
22:35 pe dx se multiply divide kiya toh bhi chalega, fir limits kaise manage karenge??? Pls reply...
Yahan dx se multiply divide is same as writing d(sinx) as cosxdx.... Moment you made it integral wrt dx, limits will change as pr x kahan se kahan vary kr rha hai... Best wishes❤❤❤
@@kaliaiit ohh thanks Bhai🙏🔥
Root wala done and dusted
Root Cos & Sin waala sawaal Done & Dusted 😌
pdf not downloading
Done and dusted bhai 2:39 min
1:03:38
3:26,4:03
42:38
Bro without integration can I get definite integration
no, indefinite ke bina nhi hoga
root cos and sin walla done and dusted
Best math teacher 🎉🎉❤❤❤❤
❤
SIR PLS DO COORDINATE GEOMETRY ONESHOT
Ky itna enough h jee mains k liye
4:42 lecture starts
same limit wala sawal done and dusted par answer galat aaya
Sir body bna li h
Great content
Thanks really wanted it ❤
Thank you Sir
Did sir say bhencho at 1:11:46?? 😂😂😂😂
😂😂lag toh aise hin Raha hai
Waise toh ....bola h
sir class me BGM dalo
Sir, I have a doubt please clear kar dijiye...mere 12th me less than 75% aaye the aur kisi reason ki vjh se jee preparation drop year me start ki ( yaani isi year ) vo bhi late me. to nios se 12th repeat kr rha hu to ky mai ab second drop lu to nios board ke according jee advance 2026 me de skta hu..?abhi ek baar bhi advance nhi diya h.
advance sirf 2 baar de sakte hai :- with 12th class & just next year {tumne agar 12th ke sath advance NHI diya , then you are left with ONLY 1 attempt that too just next year , 2nd drop advance mai allowed NHI hai }
@@IITD-or6fw but mai 12th repeat kr rhaa hu with nios board, aur abhi ek baar bhi exam nhi diya h na to jee mains na advanced. To agr maine ek baar bhi exam nhi diya to aur mai 12th repeat kr rha hu to kaise pta chlega ki I am a dropper
@@ankush12806 repeat 12th wali chiz ka mujhe jyada idea Nhi hai , but ig vo DOB se dekhenge, on safe side u assume u are left with ONLY 1 attempt .
@@ankush12806bhai chod de nahi hoga tujse 😢
rules changed! Now you have 3 attempts for IIT advance. Refer to the circular.
And btw why are you so f***ed up?
Thanks a lot sir for this amazing session
Sir ji I couldn't take live class 😞
But I will learn from you today
4:14:42 epic moment 😂
VOTE FOR COORDINATE GEOMETRY
Sir ek lecture graphical transformation pe lete aaiye
Advanced 2019 wala question nahi Hua koi hint de do pls
tan theta ko t ki jagah t square susbtitute karde ho jayega
BHAI PLEASE BRING ADVANCED PROBLEMS OF AOD OR DEFINITE INTEGRATION
S
3:10:08
32:39