Integral of sqrt(1 - sin 2x)

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  • Опубликовано: 7 фев 2025
  • In this video we will solve integral of sqrt(1 - sin 2x) w.r.t x by using simple trigonometry identities. To solve this, first we will have to get rid of the square root. To do that, we have to convert 1 - sin 2x into a perfect square.
    Following is the URL of the video explaining the derivation of trigonometric identity sin 2x = 2sin x cos x
    • sin 2x | sin(2x) | Ide...
    Other topics for the video are:
    Integral of square root of 1 - sin 2x
    What is the integral of sqrt(1 - sin 2x)?
    How to find integral of sqrt(1 - sin 2x)?
    How to evaluate integral of sqrt(1 - sin 2x)?
    You can email me at raviranjans@gmail.com
    You can follow me on facebook. My facebook account is / raviranjankumarsingh.73

Комментарии • 97

  • @3bu
    @3bu Год назад +3

    أنا عربي لم افهم اللغة لكني فهمت من الخطوات شكراً ❤
    I am an Arab. I did not understand the language, but I understood from the steps. Thank you

  • @chiragbiswas8850
    @chiragbiswas8850 Год назад +10

    Shouldn't the answer be like
    (Sinx + cosx)sgn(cosx - sinx) + c
    As the √(sinx-cosx)² opens up with a mod sign

    • @trueblood541
      @trueblood541 Год назад +5

      True ... We r among the few who know this

    • @chiragbiswas8850
      @chiragbiswas8850 Год назад +3

      @@trueblood541 us bro us🤜🤛🏽

    • @uselessvids6407
      @uselessvids6407 Год назад

      Can you please explain how?

    • @approxy..
      @approxy.. Год назад

      I understood the answer but didn't understand the way of representing the answer.
      Why you have written sgn b/w both the answers?

    • @studypoint7872
      @studypoint7872 Год назад

      ​@@approxy..Yes same doubt please tell

  • @aryansudhakar1208
    @aryansudhakar1208 Год назад +7

    What if sinx>cosx ???

    • @madhupmangal8269
      @madhupmangal8269 4 месяца назад

      That is why solution is wrong and we will take signum function

  • @simplechauhan9638
    @simplechauhan9638 Год назад +1

    How can you open sinx -cosx) ^2 under the root as sinx -cosx
    It will open with |sinx -cosx| and then the right answer will be sinx +cosx)sgn(cosx-sinx) 🎉🎉

  • @atharvkulkarni9201
    @atharvkulkarni9201 2 года назад +1

    Sir sin^2 x + cos^2 x - 2sinx cosx can also be written as (sinx - cosx)^2 and in that case ans is coming negative of ur answer

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      Basically the answer is absolute of cos x + sin x.
      Answer has to be positive.

  • @vkl9
    @vkl9 Год назад +2

    طلاب السادس عود هم موجودين هنا

  • @creative294
    @creative294 Год назад

    sir in the identity part...instead of cosx-sinx sinx -cosx if we do anwer is coming -ainx-cos x....since its square root we can write as (cox-sinx)^2 or (sinx-cosx)^2...both correct rigth??? but ans is coming diff

  • @SonuNigam-bw5tb
    @SonuNigam-bw5tb 4 месяца назад +1

    Okay 👍🏻👍🏻

  • @viveksaini4197
    @viveksaini4197 2 года назад +2

    Sir if we use tan expansion of sin2x formula then i'm getting diffrent answer. please explain why???

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад +1

      Actually answer is |cos x + sin x| + C
      If you are using tan x expansion then the integrand must be inform of square root of (((1 - tan x)^2)/sec^2 x)
      You can change it to square root of (((tan x - 1)^2)/sec^2 x)
      As
      (1 - tan x)^2 = (tan x - 1)^2
      You will get same answer as I got.

    • @nimish6762
      @nimish6762 2 года назад

      in many questions You can get different types of answer with different methods

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      @@nimish6762 No, answer is same |cos x + sin x| + C

  • @Rahul_Raj__
    @Rahul_Raj__ 3 года назад +1

    if we solve by taking sinx-cosx then shall we get the same marks in the exam???

    • @marrryam5845
      @marrryam5845 2 года назад

      No

    • @Rahul_Raj__
      @Rahul_Raj__ 2 года назад

      @@marrryam5845 My exams got over very earlier 😁 .... But thanks I will keep it in my mind.

    • @marrryam5845
      @marrryam5845 2 года назад +1

      😂

  • @neto_4280
    @neto_4280 2 года назад +1

    Thx sir -from Iraq

  • @rohankumarroy143
    @rohankumarroy143 3 года назад +2

    भगवान आपको हमेशा खुश रखे।

  • @shrikantmishra1739
    @shrikantmishra1739 3 года назад +1

    Thanks for your solution
    I m very glad ....🤗

  • @Jones_Samuel
    @Jones_Samuel 3 года назад +1

    Tq so much sir ❤️ love from karnataka

  • @karzzz8299
    @karzzz8299 2 года назад +1

    Why can't we take (sinx-cosx)whole squared instead of (cosx-sinx) whole squared

  • @atharvabane3124
    @atharvabane3124 2 года назад +1

    Sir you should have written mod of cosx - sinx and not just cosx - sinx.

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      Yes.

    • @atharvabane3124
      @atharvabane3124 2 года назад +1

      @@RaviRanjanKumarSingh sir so will that affect the answer. I think it will add something

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад +1

      @@atharvabane3124 Sorry! In haste I made the above comment.
      The answer is abs(cos x - sin x) + C.

  • @minamaged6197
    @minamaged6197 3 года назад +1

    great .. brief and efficient

  • @prynka1803
    @prynka1803 3 года назад +1

    Marvellous explaination 😊😇.....

  • @hussainkazmi5432
    @hussainkazmi5432 2 года назад

    Sir what abt 1/underoot 1-sin2x ?

  • @ss-rf1ow
    @ss-rf1ow 3 года назад +1

    Thanks🙏🙏🙏🙏🙏🙏

  • @lapiiaddicted
    @lapiiaddicted 3 года назад

    What'd be the answer if it was int 1√(1-sin2x) dx...

  • @sophiachacha6553
    @sophiachacha6553 2 года назад

    Guys help me plz -2sinxcosx is replaced by what coz l won't see it at the end of solution

  • @riyagaur5202
    @riyagaur5202 3 года назад +2

    Why cosx-sin x whole square why not sinx-cosx whole square???

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  3 года назад

      just to get positive result

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  3 года назад

      basically it should have been mod

    • @fardinnihal2283
      @fardinnihal2283 3 года назад +2

      @@RaviRanjanKumarSingh if we make it (sinx-cosx)^2 then the result will be {-cosx-sinx+c}

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  3 года назад

      @@fardinnihal2283 the result is an absolute value of cos x + sin x

    • @AJAY-AP1773
      @AJAY-AP1773 Год назад

      Bro actual me √(x²) = |x| , hota hai, aur mod hamesha hi positive hota hai, isliye mod ko hatane ke liye pahle se hi positive value le lene se mod nahi lagana padta

  • @abdiazizmohmud9109
    @abdiazizmohmud9109 2 года назад +1

    Thanks sir.

  • @user-ace96plays
    @user-ace96plays 2 года назад

    Thanks sir lots of love and Reception for you.

  • @dhilloncreativity825
    @dhilloncreativity825 3 года назад +1

    Thnks good explanation

  • @bambahadursinghthakuri148
    @bambahadursinghthakuri148 2 года назад +1

    Good method 👍

  • @Le-eve
    @Le-eve 2 года назад +1

    thank you 💓

  • @thousimshaik7065
    @thousimshaik7065 3 года назад +1

    Thank you good explanation

  • @aakashtiwari3212
    @aakashtiwari3212 3 года назад +2

    Bro mod bhi toh lena padta hai😶
    Root se nhikalne ke baad

  • @yafoelise4241
    @yafoelise4241 3 года назад

    Pls can u make a video on moment of inertia

  • @sureshpandey7370
    @sureshpandey7370 3 года назад +1

    Why not sinx-cosx

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  3 года назад

      Just to avoid negative sign. The answer is abs(cos x - sin x) + C.

  • @ramaobayda9727
    @ramaobayda9727 11 месяцев назад

    What if 2x_2cos.cosx

  • @bhavaniprasuna8444
    @bhavaniprasuna8444 3 года назад +1

    Thank you, sir.🙏

  • @gopalkrishan3997
    @gopalkrishan3997 4 месяца назад +1

    where is mod

  • @studypoint7872
    @studypoint7872 Год назад

    Wrong

  • @alhaji1595
    @alhaji1595 2 года назад

    اصعب شي تكامل الدوال المثلثية

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      I didn't get you. Please write in English.

    • @alhaji1595
      @alhaji1595 2 года назад +1

      @@RaviRanjanKumarSinghmy bad I was talking to my friend who will going to see this video. And thanks you for teaching us science that teachers couldn't teach it to us

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      @@alhaji1595 You are welcome!

  • @madhupmangal8269
    @madhupmangal8269 4 месяца назад

    It is wrong solution

    • @madhupmangal8269
      @madhupmangal8269 4 месяца назад

      Can check the answer in the respective first book also

  • @rajivranjanmandal6901
    @rajivranjanmandal6901 3 года назад

    Mod ko kha gya kya
    🤬#&$@®•

  • @genuinepathasala
    @genuinepathasala Год назад +1

    Thank you sir

  • @beautytiwari8339
    @beautytiwari8339 2 года назад +1

    Why not sinx-cosx

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      Yes you can go with it.

    • @beautytiwari8339
      @beautytiwari8339 2 года назад +1

      @@RaviRanjanKumarSingh but then sign will be different
      -cosx-sinx+c would be the answer

    • @RaviRanjanKumarSingh
      @RaviRanjanKumarSingh  2 года назад

      @@beautytiwari8339 The actual answer is |sin x + cos x| + C

    • @beautytiwari8339
      @beautytiwari8339 2 года назад

      @@RaviRanjanKumarSingh oh kay got it 👍 square root always gives mod 👍👍