What is the integral from 0 to 3/2 of xcos(pi)x ?

The integral from 0 to 3/2 of xcos(pi)x is -9/8

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integral from 0 to 3/2 of xcos(pi)x

\int_{0}^{\frac{3}{2}} x cos (π) x d x

- \frac{9}{8}

Decimal

- 1.125

Solution steps

\int_{0}^{\frac{3}{2}} 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_{0}^{\frac{3}{2}} xx d x

cos (π) = - 1

= (- 1) \cdot \int_{0}^{\frac{3}{2}} xx d x

Simplify

xx : x^{2}

= (- 1) \cdot \int_{0}^{\frac{3}{2}} x^{2} d x

Apply the Power Rule

= (- 1) [\frac{x ^{3}}{3}]_{0}^{\frac{3}{2}}

Simplify

= - [\frac{x ^{3}}{3}]_{0}^{\frac{3}{2}}

Compute the boundaries:

\frac{9}{8}

= - \frac{9}{8}

What is the integral from 0 to 3/2 of xcos(pi)x ?
The integral from 0 to 3/2 of xcos(pi)x is -9/8