zned6559
  • zned6559
Please help I will medal why does d/dx S from 0 to pi cosx^2 dx=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zned6559
  • zned6559
\[\frac{ d }{ dx }\int\limits_{0}^{\pi}cosx^2dx = 0\]
zned6559
  • zned6559
why does it equal zero???
Michele_Laino
  • Michele_Laino
since the integral is a real number

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Michele_Laino
  • Michele_Laino
and not a function
zned6559
  • zned6559
i still don't get it
zned6559
  • zned6559
what does it mean when d/dx is on the outside versus being on the inside of the integral?
Michele_Laino
  • Michele_Laino
we can write this: \[\frac{d}{{dx}}\int_0^\pi {{{\left( {\cos x} \right)}^2}} dx = \frac{d}{{dx}}\left. {\left( {\frac{{x + \sin x\cos x}}{2}} \right)} \right|_0^\pi = \frac{d}{{dx}}\left( {\frac{\pi }{2}} \right) = 0\]
zned6559
  • zned6559
how did you get the stuff inside the parenthesis?
Michele_Laino
  • Michele_Laino
I have used this identity: \[{\left( {\cos x} \right)^2} = \frac{{1 + \cos \left( {2x} \right)}}{2}\]
ganeshie8
  • ganeshie8
If we pretend that d/dx isn't there, would you agree that definite integral evaluates to some real number ?
zned6559
  • zned6559
yes
ganeshie8
  • ganeshie8
whats the derivative of a real number ?
zned6559
  • zned6559
0
zned6559
  • zned6559
so what if the d/dx is on the inside?
ganeshie8
  • ganeshie8
it isn't on the inside
ganeshie8
  • ganeshie8
it is outside to make your life easy :)
ganeshie8
  • ganeshie8
if it is inside, you will have to find the derivative first and then evaluate the integral

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