Question

integrate the following

Answer 1

\[\int\limits_{0}^{\Pi/2} \sin ^{2}x \div (\sin ^{2}x+4\cos ^{2}x)\]

Answer 2

change cos^2 = 1 - sin^2

Answer 3

so you have for the denominator
sin^2 + 4(1-sin^2) =
sin^2 + 4 - 4 sin^2
-3sin^2 + 4

Answer 4

I think this is aprtial fractions.
If you take cos^2 x common from denominator you have
tan^2 x/(tan^2 x+4) Put tan x=t.
you'll get dx=dt/sec^2 x= dt/(1+t^2).
So you have t^2/((t^2+4)(t^2+1)). Do you know partial fractions?

Answer 5

you dont need partional fractions

Answer 6

How will you do it by converting denominator to sin?

Answer 7

the denominator is -3sin^2 t + 4 , do long division

Answer 8

we gottta use the properties of definite integrals

Answer 9

shank, change cos^2 = 1 - sin^2

Answer 10

And then what?

Answer 11

long division

Answer 12

?