integral from 0 to pi/4 of 3sec^2(x)

解答

\int_{0}^{\frac{π}{4}} 3 sec^{2} (x) d x

3

求解步骤

\int_{0}^{\frac{π}{4}} 3 sec^{2} (x) d x

提出常数:

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

= 3 \cdot \int_{0}^{\frac{π}{4}} sec^{2} (x) d x

使用积分常见定则:

\int sec^{2} (x) d x = tan (x)

= 3 [tan (x)]_{0}^{\frac{π}{4}}

带入上下限计算后得:

1

= 3 \cdot 1

化简

= 3

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