integral from 0 to 4 of e^xsin(x)

解答

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

\frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 ) + 1}{2}

十进制

- 2.31614 \dots

求解步骤

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

计算不定积分:

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

带入上下限计算后得:

\int_{0}^{4} e^{x} sin (x) d x = \frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 )}{2} - (- \frac{1}{2})

= \frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 )}{2} - (- \frac{1}{2})

化简

= \frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 ) + 1}{2}

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