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

解答

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

\frac{9}{4}

十进制

2.25

求解步骤

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

使用三角恒等式改写

= \int_{0}^{\frac{π}{3}} (1 + tan^{2} (x)) tan^{3} (x) d x

使用换元积分法

= \int_{0}^{3} u^{3} d u

使用幂法则

= [\frac{u ^{4}}{4}]_{0}^{3}

带入上下限计算后得:

\frac{9}{4}

= \frac{9}{4}

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