Question

Sub. Formula to evaluate the integral. posted below (2 problems)

Answer 1

problem one
\[\int\limits_{0}^{\pi} (1 + \cos5t)^2 \sin5t dt\]
problem two
\[\int\limits_{\pi/6}^{\pi/2} \cot x \csc^3 x dx\]

Answer 2

first problem, let \[\large u=1+\cos 5t;\space du=-5\sin 5tdt\]
second problem, rewrite the problem as \[\large \int\limits_{\pi/6}^{\pi/2}\csc ^2 x (\csc x \cot x dx)\] and use the substitution \[\large u=\csc x;\space du=-\csc x \cot x dx\]

in both cases, after integration, return to the original variable x then sub the limits of integration

Answer 3

oh alright, thanks a lot