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受欢迎的微积分 >

integral from 0 to 2 of 2pix(x^2)

解答

\int_{0}^{2} 2 π x (x^{2}) d x

解答

8 π

+1

十进制

25.13274 \dots

求解步骤

\int_{0}^{2} 2 π x x^{2} d x

提出常数:

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

= 2 π \cdot \int_{0}^{2} x x^{2} d x

化简

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

= 2 π \cdot \int_{0}^{2} x^{3} d x

使用幂法则

= 2 π [\frac{x ^{4}}{4}]_{0}^{2}

带入上下限计算后得:

4

= 2 π 4

化简

= 8 π

作图

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