integral from 0 to pi of 5e^xsin(x)

解答

\int_{0}^{π} 5 e^{x} sin (x) d x

\frac{5 e ^{π} + 5}{2}

十进制

60.35173 \dots

求解步骤

\int_{0}^{π} 5 e^{x} sin (x) d x

计算不定积分:

\int 5 e^{x} sin (x) d x = 5 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) + C

带入上下限计算后得:

\int_{0}^{π} 5 e^{x} sin (x) d x = 5 \cdot \frac{e ^{π}}{2} - (- \frac{5}{2})

= 5 \cdot \frac{e ^{π}}{2} - (- \frac{5}{2})

化简

= \frac{5 e ^{π} + 5}{2}

n = 1 \sum \infty 2

d er i v a t i v e (\frac{x + 6}{x - 6})^{5}

\frac{d}{d x} (e^{- \frac{x}{3}})

\int (1 - x^{2})^{2} x^{2} d x

a re a y = 3 x^{4} - 3 x^{2}, y = 8 x^{2}