What is the integral from-pi/4 to pi/4 of sin(x)-e^x ?

The integral from-pi/4 to pi/4 of sin(x)-e^x is -(e^{pi/4}-1/(e^{pi/4)})

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integral from-pi/4 to pi/4 of sin(x)-e^x

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) - e^{x} d x

- (e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}})

Decimal Notation

- 1.73734 \dots

Solution steps

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) - e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) d x - \int_{- \frac{π}{4}}^{\frac{π}{4}} e^{x} d x

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) d x = 0

\int_{- \frac{π}{4}}^{\frac{π}{4}} e^{x} d x = e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}}

= 0 - (e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}})

Simplify

= - (e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}})

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What is the integral from-pi/4 to pi/4 of sin(x)-e^x ?
The integral from-pi/4 to pi/4 of sin(x)-e^x is -(e^{pi/4}-1/(e^{pi/4)})