1. ## evaluating the integral

Evaluate the integral using u substitution.

Integral of (cos(x))^25 sin(x) dx; use u = cos(x)

I obtained (cos(x))^26/26. However, there is a negative in the solution and I am unsure of how there is a negative.

Unless since u = cos x, and you plug in du, then do you do the derivative of sin and get - cos which results int he negative?

2. Originally Posted by masterofcheese
Evaluate the integral using u substitution.

Integral of (cos(x))^25 sin(x) dx; use u = cos(x)

I obtained (cos(x))^26/26. However, there is a negative in the solution and I am unsure of how there is a negative.

Unless since u = cos x, and you plug in du, then do you do the derivative of sin and get - cos which results int he negative?
$\displaystyle \int cos^{25}(x)sin(x)dx$

$\displaystyle u=cos(x)$

$\displaystyle \frac{du}{dx}=-sin(x)$

$\displaystyle dx=\frac{du}{-sin(x)}$

The integral becomes:

$\displaystyle -\int u^{25}du$

So your answer should be negative since the derivative of cos(x) is negative.