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

The integral from 0 to 2 of e^{2x}+x^4 is (e^4-1)/2+32/5

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

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

\frac{e ^{4} - 1}{2} + \frac{32}{5}

Decimal

33.19907 \dots

Solution steps

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

\int_{0}^{2} e^{2 x} d x = \frac{e ^{4} - 1}{2}

\int_{0}^{2} x^{4} d x = \frac{32}{5}

= \frac{e ^{4} - 1}{2} + \frac{32}{5}

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What is the integral from 0 to 2 of e^{2x}+x^4 ?
The integral from 0 to 2 of e^{2x}+x^4 is (e^4-1)/2+32/5