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integral from 0 to 1 of pi(2x)^2

解答

\int_{0}^{1} π (2 x)^{2} d x

解答

\frac{4 π}{3}

+1

十进制

4.18879 \dots

求解步骤

\int_{0}^{1} π (2 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}^{1} (2 x)^{2} d x

化简

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

= π \cdot \int_{0}^{1} 4 x^{2} d x

提出常数:

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

= π 4 \cdot \int_{0}^{1} x^{2} d x

使用幂法则

= π 4 [\frac{x ^{3}}{3}]_{0}^{1}

带入上下限计算后得:

\frac{1}{3}

= π 4 \cdot \frac{1}{3}

化简

= \frac{4 π}{3}

作图

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