integral from-6 to 6 of (e^θ+sin(θ))

解答

\int_{- 6}^{6} (e^{θ} + sin (θ)) d θ

e^{6} - \frac{1}{e ^{6}}

十进制

403.42631 \dots

求解步骤

\int_{- 6}^{6} e^{θ} + sin (θ) d θ

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_{- 6}^{6} e^{θ} d θ + \int_{- 6}^{6} sin (θ) d θ

\int_{- 6}^{6} e^{θ} d θ = e^{6} - \frac{1}{e ^{6}}

\int_{- 6}^{6} sin (θ) d θ = 0

= e^{6} - \frac{1}{e ^{6}} + 0

化简

= e^{6} - \frac{1}{e ^{6}}

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