integral from-pi/2 to pi/2 of (cos(x)-2)

解答

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 2) d x

2 - 2 π

十进制

- 4.28318 \dots

求解步骤

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 2 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x - \int_{- \frac{π}{2}}^{\frac{π}{2}} 2 d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x = 2

\int_{- \frac{π}{2}}^{\frac{π}{2}} 2 d x = 2 π

= 2 - 2 π

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

\int_{2}^{5} 2^{4 x} d x

\int_{0}^{2} \frac{x + 1}{x ^{2} + 1} d x

\int_{0}^{1} 2 + 3 x d x

\int_{0}^{1} (x^{3} - 2 x^{2} + x + 2) d x