What is the integral from-2 to 0 of (20x-e^x) ?

The integral from-2 to 0 of (20x-e^x) is 1/(e^2)-41

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integral from-2 to 0 of (20x-e^x)

\int_{- 2}^{0} (20 x - e^{x}) d x

\frac{1}{e ^{2}} - 41

Decimal

- 40.86466 \dots

Solution steps

\int_{- 2}^{0} 20 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_{- 2}^{0} 20 x d x - \int_{- 2}^{0} e^{x} d x

\int_{- 2}^{0} 20 x d x = - 40

\int_{- 2}^{0} e^{x} d x = 1 - \frac{1}{e ^{2}}

= - 40 - (1 - \frac{1}{e ^{2}})

Simplify

= \frac{1}{e ^{2}} - 41

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What is the integral from-2 to 0 of (20x-e^x) ?
The integral from-2 to 0 of (20x-e^x) is 1/(e^2)-41