Question

Evaluate the following integral:

Answer 1

\[\int\limits_{\pi/3}^{\pi/2}\frac{ 1+\sin^2x }{ \sin^2x }dx\]

Answer 2

split up the fraction ... evaluate it separately.

Answer 3

That's when I get stuck...

\[\int\limits_{\pi/3}^{\pi/2}\frac{ 1 }{ \sin^2x } + \int\limits_{\pi/3}^{\pi/2}\frac{ \sin^2x }{ \sin^2x }\]

Answer 4

How do I find out the integral of 1/sin^2x?

Answer 5

= csc^2(x) = 1 + cot^2(x) ..

Answer 6

Isn't it just cot^2x for the integral of csc^2x? Why do you have 1 in there?

Answer 7

\[\int\frac{1}{\sin^2x}\mathrm dx=\int\csc^2 x\mathrm dx=-\cot x\]

Answer 8

sorry .. my bad!!

Answer 9

Great thanks people.