You are not ready for hard math if you do not understand this problem
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- Опубликовано: 8 сен 2024
- In this video, I am working on this killer calculus problem from Korean SAT Math. With this problem, we use challenging integral, with advanced calculus skills to get areas, and also the trigonometric functions to deal with for the final answer. See if you understand this problem for hard math.
#integral #calculus #koreansatmath
Hello all. At 5:55, I accidentally put = sign, where I was supposed to put an arrow sign as I am getting the integral of f(x) from 2 to 4 by using the integral of g(2x) from 1 to 2, so they are not equal. My bad for mistakenly putting = sign. Enjoy!
Figured professor. Your work is just great
I don't understand why the integral of f(x) from 2 to 4 is equal to the integral of g(2x) from 1 to 2, using the condition that g(2x)=2f(x).
I get lost because you found that the integral of f(x) from 2 to 4 is equal to 5/2, and then you found later that the area (which should be the same as the integral) is equal to 7.
Similarly, I don't understand why the integral of f(x) from 4 to 8 is equal to the integral of g(2x) from 2 to 4, using the condition that g(2x)=2f(x).
Thats really basic one, change of boundaries. Look at what g(x) is
@@pietergeerkens6324 To me, I believe Dr PK applied some technique that is more relevant to time-test taking strategy. I got to figure this out by knowing an area of an inverse function is to look at y-axis just like when you look at x-axis for the area of regular f(x). Then, everything seems so logical and nice. But guess what, it took quite a bit of time to understand this too
Yes i also had problem in understanding it 😢
@@himanshukumar8881 Seems like DR PK used geometric approach along with the calculus so it requires some high level mathematical understanding as Peter said. Having geometric eye is the key on DR PK's solution here
@@MrGLA-zs8xt yes but he has to give some hint how integration of f(x) from 2 to 4 = integration g(2x) from 1 to 2 .
Wow you're really good. I always enjoy your videos
Haha thanks a lot my friend for your support! I really appreciate it👍👍👍
Professor is there any direct relationship between integration of function and its inverse.
Say f(x) = x^2 it's inverse f^-1= √x
The integration of f(x) form 1 to 3 = ??? In terms of its inverse.
The relationship between f(x) and its inverse is f(x) =[ f^-1 (x) ] ^ 4
Hello my friend! Yes there is but that direct formula is a bit messy to memorize haha. Called Laisant formula. 👍👍👍
@@drpkmath1234 thank you professor
A hard and interesting question professor, amazing solution🙌🏻
Thanks a lot my friend for your support haha. I appreciate it👍👍👍
Man i also had followed you on twitter too
Thats great to know my friend! Thanks for the support👍👍👍
Why that curve is their while intergrating or summing up area
Hello my friend! I used the graphing method using how g(x) is an inverse of f(x)👍👍👍
Wowww, I love this question, though this was a bit hard for me
Thanks a lot my friend👍👍👍
Very professionally done prof🎉
Thanks a lot my friend haha👍👍👍
Another great video prof.
Thanks a lot my friend haha👍👍👍
I guess I'm not ready for hard math yet.. and I didn't even watch the video!
Haha go ahead and watch it my friend👍👍👍
@drpkmath1234 I watched it. I understood all of it, but I don't think I could've done it myself.
Couldnt the answer be k(139 +4) for any k equal or greater to 1?
No, not really😂😂😂
@@drpkmath1234oh i didnt see that p and q are relative prime
How integral of f(x) from 2 to 4 is 5/2 and also 7 ?
See I was getting integtal of f(x) from 2 to 4 using 5/2.👍👍👍
How do you know that f(2) = 2???
Yes I would love to know that
g(2x) is 2f(x). this is given from the question. f(1) is 1, this is also given from the question. now it is easy to see f(2) is 2.
He doesnt explain well…
it makes sense the following:
g(2) = 2f(1) = 2
Using that g is inverse of f:
g(f(2)) = 2,
Notice that g is injective.
If you don’t remember what this means: if g(x)= g(y) -> x = y.
Now we can conclude f(2) = 2, because
g(2) = 2 = g(f(2)),
Using, injectivity:
g(f(2)) = g(2) -> f(2) = 2
@@josepereira2759 i thought injective meant that for each y value possible, there is only one x value that points to it
@@hehexd9781 it is equivalent:
suppose f(x) = f(y) , since there is only one x to each f(x) and we know that f(x) = f(y), then x cannot be different from y, this means x = y.