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integral from 0 to 4 of pi(4x^2)^2

解答

\int_{0}^{4} π (4 x^{2})^{2} d x

解答

\frac{16384 π}{5}

+1

十进制

10294.37080 \dots

求解步骤

\int_{0}^{4} π (4 x^{2})^{2} d x

提出常数:

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

= π \cdot \int_{0}^{4} (4 x^{2})^{2} d x

化简

(4 x^{2})^{2} : 16 x^{4}

= π \cdot \int_{0}^{4} 16 x^{4} d x

提出常数:

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

= π 16 \cdot \int_{0}^{4} x^{4} d x

使用幂法则

= π 16 [\frac{x ^{5}}{5}]_{0}^{4}

带入上下限计算后得:

\frac{1024}{5}

= π 16 \cdot \frac{1024}{5}

化简

= \frac{16384 π}{5}

作图

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