What is the integral of x^2cos(pi)x ?

The integral of x^2cos(pi)x is -(x^4)/4+C

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integral of x^2cos(pi)x

\int x^{2} cos (π) x d x

- \frac{x ^{4}}{4} + C

Solution steps

\int x^{2} 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 x^{2} x d x

cos (π) = - 1

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

Simplify

x^{2} x : x^{3}

= (- 1) \cdot \int x^{3} d x

Apply the Power Rule

= (- 1) \frac{x ^{4}}{4}

Simplify

= - \frac{x ^{4}}{4}

Add a constant to the solution

= - \frac{x ^{4}}{4} + C