What is the integral from 0 to 2 of 8x-3+5e^{2-x} ?

The integral from 0 to 2 of 8x-3+5e^{2-x} is 5e^2+5

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integral from 0 to 2 of 8x-3+5e^{2-x}

\int_{0}^{2} 8 x - 3 + 5 e^{2 - x} d x

5 e^{2} + 5

Solution steps

\int_{0}^{2} 8 x - 3 + 5 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}^{2} 8 x d x - \int_{0}^{2} 3 d x + \int_{0}^{2} 5 e^{2 - x} d x

\int_{0}^{2} 8 x d x = 16

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

\int_{0}^{2} 5 e^{2 - x} d x = 5 (e^{2} - 1)

= 16 - 6 + 5 (e^{2} - 1)

Simplify

16 - 6 + 5 (e^{2} - 1) : 5 e^{2} + 5

= 5 e^{2} + 5

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What is the integral from 0 to 2 of 8x-3+5e^{2-x} ?
The integral from 0 to 2 of 8x-3+5e^{2-x} is 5e^2+5