What is the integral from 0 to 3 of 3x^2+4e^{-2x} ?

The integral from 0 to 3 of 3x^2+4e^{-2x} is -2/(e^6)+29

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integral from 0 to 3 of 3x^2+4e^{-2x}

\int_{0}^{3} 3 x^{2} + 4 e^{- 2 x} d x

- \frac{2}{e ^{6}} + 29

Decimal

28.99504 \dots

Solution steps

\int_{0}^{3} 3 x^{2} + 4 e^{- 2 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_{0}^{3} 3 x^{2} d x + \int_{0}^{3} 4 e^{- 2 x} d x

\int_{0}^{3} 3 x^{2} d x = 27

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

= 27 + 2 (1 - \frac{1}{e ^{6}})

Simplify

27 + 2 (1 - \frac{1}{e ^{6}}) : - \frac{2}{e ^{6}} + 29

= - \frac{2}{e ^{6}} + 29

What is the integral from 0 to 3 of 3x^2+4e^{-2x} ?
The integral from 0 to 3 of 3x^2+4e^{-2x} is -2/(e^6)+29