What is the integral from 0 to 2 of 3x^2-2x+7e^x ?

The integral from 0 to 2 of 3x^2-2x+7e^x is 7e^2-3

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integral from 0 to 2 of 3x^2-2x+7e^x

\int_{0}^{2} 3 x^{2} - 2 x + 7 e^{x} d x

7 e^{2} - 3

Decimal

48.72339 \dots

Solution steps

\int_{0}^{2} 3 x^{2} - 2 x + 7 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_{0}^{2} 3 x^{2} d x - \int_{0}^{2} 2 x d x + \int_{0}^{2} 7 e^{x} d x

\int_{0}^{2} 3 x^{2} d x = 8

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} 7 e^{x} d x = 7 (e^{2} - 1)

= 8 - 4 + 7 (e^{2} - 1)

Simplify

8 - 4 + 7 (e^{2} - 1) : 7 e^{2} - 3

= 7 e^{2} - 3

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What is the integral from 0 to 2 of 3x^2-2x+7e^x ?
The integral from 0 to 2 of 3x^2-2x+7e^x is 7e^2-3