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受欢迎的微积分 >

integral from x to 1 of 1/(1+x^2)

解答

\int_{x}^{1} \frac{1}{1 + x ^{2}} d x

解答

\frac{π}{4} - arctan (x)

求解步骤

\int_{x}^{1} \frac{1}{1 + x ^{2}} d x

使用积分常见定则:

\int \frac{1}{1 + x ^{2}} d x = arctan (x)

= [arctan (x)]_{x}^{1}

带入上下限计算后得:

\frac{π}{4} - arctan (x)

= \frac{π}{4} - arctan (x)

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