What is the integral of (pi-x)cos(pi)x ?

The integral of (pi-x)cos(pi)x is -(pix^2)/2+(x^3)/3+C

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integral of (pi-x)cos(pi)x

\int (π - x) cos (π) x d x

- \frac{π x ^{2}}{2} + \frac{x ^{3}}{3} + C

Solution steps

\int (π - x) cos (π) x d x

Take the constant out:

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

= cos (π) \cdot \int (π - x) x d x

cos (π) = - 1

= (- 1) \cdot \int (π - x) x d x

Expand

(π - x) x : π x - x^{2}

= (- 1) \cdot \int π x - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= (- 1) (\int π x d x - \int x^{2} d x)

\int π x d x = \frac{π x ^{2}}{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= (- 1) (\frac{π x ^{2}}{2} - \frac{x ^{3}}{3})

Simplify

= - \frac{π x ^{2}}{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= - \frac{π x ^{2}}{2} + \frac{x ^{3}}{3} + C

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What is the integral of (pi-x)cos(pi)x ?
The integral of (pi-x)cos(pi)x is -(pix^2)/2+(x^3)/3+C