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

解答

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

- \frac{81 f}{4}

求解步骤

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

提出常数:

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

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

化简

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

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

使用幂法则

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

带入上下限计算后得:

- \frac{81}{4}

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

化简

= - \frac{81 f}{4}

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