What is the integral from-2 to 0 of (3x-2e^x) ?

The integral from-2 to 0 of (3x-2e^x) is 2/(e^2)-8

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integral from-2 to 0 of (3x-2e^x)

\int_{- 2}^{0} (3 x - 2 e^{x}) d x

\frac{2}{e ^{2}} - 8

Decimal Notation

- 7.72932 \dots

Solution steps

\int_{- 2}^{0} 3 x - 2 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} 3 x d x - \int_{- 2}^{0} 2 e^{x} d x

\int_{- 2}^{0} 3 x d x = - 6

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

= - 6 - 2 (1 - \frac{1}{e ^{2}})

Simplify

- 6 - 2 (1 - \frac{1}{e ^{2}}) : \frac{2}{e ^{2}} - 8

= \frac{2}{e ^{2}} - 8

\int_{0}^{2} - x^{3} + x^{2} + 2 x d x

\int_{0}^{8} ∣ x - 3 ∣ d x

\int_{0}^{1} 4 x - 6 (x^{2})^{\frac{1}{3}} d x

\int_{- 1}^{3} (3 x - 5) (x + 2) d x

\int_{- 3}^{2} x^{2} - (6 - x) d x

What is the integral from-2 to 0 of (3x-2e^x) ?
The integral from-2 to 0 of (3x-2e^x) is 2/(e^2)-8