What is the integral from-3 to 0 of xf(x^2) ?

The integral from-3 to 0 of xf(x^2) is -(81f)/4

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integral from-3 to 0 of xf(x^2)

\int_{- 3}^{0} x f (x^{2}) d x

- \frac{81 f}{4}

Solution steps

\int_{- 3}^{0} x f x^{2} d x

Take the constant out:

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

= f \cdot \int_{- 3}^{0} x x^{2} d x

Simplify

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

= f \cdot \int_{- 3}^{0} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{- 3}^{0}

= f [\frac{x ^{4}}{4}]_{- 3}^{0}

Compute the boundaries:

- \frac{81}{4}

= f (- \frac{81}{4})

Simplify

= - \frac{81 f}{4}

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What is the integral from-3 to 0 of xf(x^2) ?
The integral from-3 to 0 of xf(x^2) is -(81f)/4