integral from-2 to 1 of 1/((11+5x)^3)

解答

\int_{- 2}^{1} \frac{1}{( 11 + 5 x ) ^{3}} d x

\frac{51}{512}

十进制

0.099609375

求解步骤

\int_{- 2}^{1} \frac{1}{( 11 + 5 x ) ^{3}} d x

使用换元积分法

= \int_{1}^{16} \frac{1}{5 u ^{3}} d u

提出常数:

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

= \frac{1}{5} \cdot \int_{1}^{16} \frac{1}{u ^{3}} d u

使用幂法则

= \frac{1}{5} [- \frac{1}{2 u ^{2}}]_{1}^{16}

带入上下限计算后得:

\frac{255}{512}

= \frac{1}{5} \cdot \frac{255}{512}

化简

= \frac{51}{512}

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