Question

Evaluate the following limit

I=∫ sinx/(1+cos^2x) dx

Answer 1

Evaluate the limit or compute the integral =

Answer 2

oh sorry about that its evaluate the integral

Answer 3

yes I understand now, substitute u=cos(x) and then try to make the integral more suitable for you.

Answer 4

\[\Large u=\cos x \longrightarrow \frac{du}{dx}=-\sin x
\\ \Large \therefore \ -\frac{du}{dx}=\sin x\]

Answer 5

Substitute that back into your integral and simplify, then you come up with a more familiar expression.

Answer 6

its \[\cos ^{2}x\] doesn't that make a difference if we do u=cosx

Answer 7

nope it doesn't in fact it's working as intended, you make this substitute to see if you become an easier integral, try it and see what you come up with.

Answer 8

if you substitute the entire denominator you have to apply the chain rule to the derivative, and that isn't any help at this integral.

Answer 9

if you need additional help let me know