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受欢迎的微积分 >

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

解答

\int_{0}^{1} π (x)^{2} d x

解答

\frac{π}{2}

+1

十进制

1.57079 \dots

求解步骤

\int_{0}^{1} π (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} (x)^{2} d x

化简

(x)^{2} : x

= π \cdot \int_{0}^{1} x d x

使用幂法则

= π [\frac{x ^{2}}{2}]_{0}^{1}

带入上下限计算后得:

\frac{1}{2}

= π \frac{1}{2}

化简

= \frac{π}{2}

作图

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