integral from 0 to sin(x) of 4sqrt(t)

解答

\int_{0}^{s i n (x)} 4 t d t

\frac{8}{3} sin^{\frac{3}{2}} (x)

求解步骤

\int_{0}^{s i n (x)} 4 t d t

提出常数:

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

= 4 \cdot \int_{0}^{s i n (x)} t d t

使用幂法则

= 4 [\frac{2}{3} t^{\frac{3}{2}}]_{0}^{s i n (x)}

带入上下限计算后得:

\frac{2}{3} sin^{\frac{3}{2}} (x)

= 4 \cdot \frac{2}{3} sin^{\frac{3}{2}} (x)

化简

= \frac{8}{3} sin^{\frac{3}{2}} (x)

7 x (x + 5 y) (\frac{d y}{d x}) = 7 y (x - 5 y)

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 36 )}

\frac{d}{d x} (- e^{5 x})

t an g e n t y = \frac{1}{3 + 2 x}, (2, \frac{1}{7})

(sin (π) x)^{^{'}}