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受欢迎的微积分 >

integral from-1 to 1 of 2/(sqrt(4-x^2))

解答

\int_{- 1}^{1} \frac{2}{4 - x ^{2}} d x

解答

\frac{2 π}{3}

+1

十进制

2.09439 \dots

求解步骤

\int_{- 1}^{1} \frac{2}{4 - x ^{2}} d x

提出常数:

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

= 2 \cdot \int_{- 1}^{1} \frac{1}{4 - x ^{2}} d x

使用三角换元法

= 2 \cdot \int_{- \frac{π}{6}}^{\frac{π}{6}} 1 d u

常数积分:

\int a d x = a x

= 2 [1 \cdot u]_{- \frac{π}{6}}^{\frac{π}{6}}

化简

= 2 [u]_{- \frac{π}{6}}^{\frac{π}{6}}

带入上下限计算后得:

\frac{π}{3}

= 2 \cdot \frac{π}{3}

化简

= \frac{2 π}{3}

作图

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