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integral from 0 to 3 of pi(4x)^2

解答

\int_{0}^{3} π (4 x)^{2} d x

解答

144 π

+1

十进制

452.38934 \dots

求解步骤

\int_{0}^{3} π (4 x)^{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}^{3} (4 x)^{2} d x

化简

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

= π \cdot \int_{0}^{3} 16 x^{2} 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}^{3} x^{2} d x

使用幂法则

= π 16 [\frac{x ^{3}}{3}]_{0}^{3}

带入上下限计算后得:

9

= π 16 \cdot 9

化简

= 144 π

作图

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