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Math Help - evaluating the integral

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by masterofcheese View Post
    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?
    \int cos^{25}(x)sin(x)dx

    u=cos(x)

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

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

    The integral becomes:

    -\int u^{25}du

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