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

The integral from 0 to 2 of (x^3-2x+e^x) is e^2-1

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

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

e^{2} - 1

Decimal

6.38905 \dots

Solution steps

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

\int_{0}^{2} x^{3} d x = 4

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

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

= 4 - 4 + e^{2} - 1

Simplify

= e^{2} - 1

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What is the integral from 0 to 2 of (x^3-2x+e^x) ?
The integral from 0 to 2 of (x^3-2x+e^x) is e^2-1