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

change cos^2 = 1 - sin^2

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

you dont need partional fractions

How will you do it by converting denominator to sin?

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

we gottta use the properties of definite integrals

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

And then what?

long division

|dw:1328867815825:dw|

You're effectively doing the same thing only.

|dw:1328867933423:dw|

ok you did trig substitution

i see that, im asking about your t = tan x part

what sort of substitution is this called?

Yeah thats a trignometric substituion.

ok your solution is better, im not sure if i would go ahead with mine . not sure what do do next

you can divide top and bottom by cos^2 for my solution

shank, can i ask a simple question about kites

hmmm ok.