A calculus problem by Vinay Agarwal
If ∫ 0 π / 2 a 2 cos 2 x + b 2 sin 2 x d x = 2 a b π , then find the value of ∫ 0 π / 2 ( 4 cos 2 x + 9 sin 2 x ) 2 d x .
The answer is 0.047269.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
I Too did the same!!
Log in to reply
can you give a little more insight on it , plz ? :)
Log in to reply
Consider the first equation to be a function of a and b rather than x .
Then differentiate once wrt a and then once wrt b both sides .
Take somethings to RHS And add both equations to get the result!
Log in to reply
@Prakhar Bindal – lekin bhai phir wo integral sign toh hat gya , apne ko to wahi chahiya tha :~\
Log in to reply
@A Former Brilliant Member – Nope wo tab hatega agar tu x ke respect be differentiate karega . a aur b ke respect mein nhi
Log in to reply
@Prakhar Bindal – achaaaaaaaa..... han bhai aa gya samaj , thik-thik , fenyman trick ki tarah , hai na ?
Log in to reply
@A Former Brilliant Member – exactly!!!
Log in to reply
@Prakhar Bindal – thank you bhai :)
I think it has to be differentiated w.r.t 'a' AND 'b'.
It is
Pi/4ab(1/a^2 +1/b^2) Put and get answer.
Hint. Differentiate both sides with respect to 'a' or 'b'