integral from 0 to pi/6 of (9sec^2(x))

解答

\int_{0}^{\frac{π}{6}} (9 sec^{2} (x)) d x

33

十进制

5.19615 \dots

求解步骤

\int_{0}^{\frac{π}{6}} 9 sec^{2} (x) d x

提出常数:

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

= 9 \cdot \int_{0}^{\frac{π}{6}} sec^{2} (x) d x

使用积分常见定则:

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

= 9 [tan (x)]_{0}^{\frac{π}{6}}

带入上下限计算后得:

\frac{1}{3}

= 9 \cdot \frac{1}{3}

化简

= 33

\int \frac{1}{7 - 3 x} d x

y^{^{'}} = 9 x + y

(2 e^{y} - x) (\frac{d y}{d x}) = 1

d er i v a t i v e f (x) = - 7 e^{- 3 x} - 6 e^{- 3 x} x

x \to 3 lim (\frac{x ^{2} - 8}{x - 3})