$int_(pi/4)^(pi/2)(-e^(cotx))/(sin^2x)dx=$ ?

Question

I used u-sub for this one, and I got $1/2-1/2e^2$ . However, the correct answer is $1-e$ .

Is my answer wrong or I need to simplify it? If so, how?

Thank you!

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Answer 1 · 2018-04-10T05:05:40

$int_(pi/4)^(pi/2)(-e^(cotx))/(sin^2x)dx=1-e$

For $int_(pi/4)^(pi/2)(-e^(cotx))/(sin^2x)dx$ , let $u=cotx$

then $du=-csc^2xdx$ and upper and lower limits are $0$ and $1$ respectively. And

$int_(pi/4)^(pi/2)(-e^(cotx))/(sin^2x)dx$

= $int_1^0e^udu$

= $[e^u]_1^0$

= $1-e$