What is the integral from-pi to 0 of cos(n)x ?

The integral from-pi to 0 of cos(n)x is -(pi^2)/2 cos(n)

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integral from-pi to 0 of cos(n)x

\int_{- π}^{0} cos (n) x d x

- \frac{π ^{2}}{2} cos (n)

Solution steps

\int_{- π}^{0} cos (n) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (n) \cdot \int_{- π}^{0} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- π}^{0}

= cos (n) [\frac{x ^{2}}{2}]_{- π}^{0}

Compute the boundaries:

- \frac{π ^{2}}{2}

= cos (n) (- \frac{π ^{2}}{2})

Simplify

= - \frac{π ^{2}}{2} cos (n)

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What is the integral from-pi to 0 of cos(n)x ?
The integral from-pi to 0 of cos(n)x is -(pi^2)/2 cos(n)