What is the integral from-6 to 6 of (e^θ+sin(θ)) ?

The integral from-6 to 6 of (e^θ+sin(θ)) is e^6-1/(e^6)

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integral from-6 to 6 of (e^θ+sin(θ))

\int_{- 6}^{6} (e^{θ} + sin (θ)) d θ

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

Decimal Notation

403.42631 \dots

Solution steps

\int_{- 6}^{6} e^{θ} + sin (θ) d θ

Apply the Sum Rule:

\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

Simplify

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

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What is the integral from-6 to 6 of (e^θ+sin(θ)) ?
The integral from-6 to 6 of (e^θ+sin(θ)) is e^6-1/(e^6)