# Thread: another integration by substitution question

1. ## another integration by substitution question

Use substitution to evaluate the integral:
the integral of Π/4 to 3Π/4 of cot x dx

So far, I have that u = cot x , du = -csc x squared, and dx = -1/(cscx squared)

Thanks for any help

2. Originally Posted by turtle
Use substitution to evaluate the integral:
the integral of Π/4 to 3Π/4 of cot x dx

So far, I have that u = cot x , du = -csc x squared, and dx = -1/(cscx squared)

Thanks for any help
The integral,
$\int \cot x dx = \int \frac{\cos x}{\sin x}dx$
Let,
$u=\sin x$.
Thus,
$-\int \frac{1}{u} du$
Thus,
$-\ln |u|+C=-\ln |\sin x|$