integral from 0 to sin(x) of (1+cos(x))

解答

\int_{0}^{s i n (x)} (1 + cos (x)) d x

sin (x) + sin (sin (x))

求解步骤

\int_{0}^{s i n (x)} 1 + cos (x) 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_{0}^{s i n (x)} 1 d x + \int_{0}^{s i n (x)} cos (x) d x

\int_{0}^{s i n (x)} 1 d x = sin (x)

\int_{0}^{s i n (x)} cos (x) d x = sin (sin (x))

= sin (x) + sin (sin (x))

\int_{1}^{2} 4 x (x^{2} + 2) d x

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

\int_{0}^{\frac{π}{2}} \frac{1 + cos ( 2 t )}{2} d t

\int_{0}^{\frac{x}{4}} sin (4 t) d t

\int_{1}^{2} \frac{1}{6 x} d x