What is the integral of picos(pi)x ?

The integral of picos(pi)x is -(pix^2)/2+C

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integral of picos(pi)x

\int π cos (π) x d x

- \frac{π x ^{2}}{2} + C

Solution steps

\int π cos (π) x d x

Take the constant out:

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

= π cos (π) \cdot \int x d x

π cos (π) = - π

= (- π) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= (- π) \frac{x ^{2}}{2}

Simplify

(- π) \frac{x ^{2}}{2} : - \frac{π x ^{2}}{2}

= - \frac{π x ^{2}}{2}

Add a constant to the solution

= - \frac{π x ^{2}}{2} + C

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