What is the integral from 0 to 2 of ((x^2)/2+2) ?

The integral from 0 to 2 of ((x^2)/2+2) is 16/3

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integral from 0 to 2 of ((x^2)/2+2)

\int_{0}^{2} (\frac{x ^{2}}{2} + 2) d x

\frac{16}{3}

Decimal Notation

5.33333 \dots

Solution steps

\int_{0}^{2} \frac{x ^{2}}{2} + 2 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} \frac{x ^{2}}{2} d x + \int_{0}^{2} 2 d x

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

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

= \frac{4}{3} + 4

Simplify

\frac{4}{3} + 4 : \frac{16}{3}

= \frac{16}{3}

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What is the integral from 0 to 2 of ((x^2)/2+2) ?
The integral from 0 to 2 of ((x^2)/2+2) is 16/3