What is the integral from 0 to 1 of 1/2 x^3+2 ?

The integral from 0 to 1 of 1/2 x^3+2 is 17/8

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integral from 0 to 1 of 1/2 x^3+2

\int_{0}^{1} \frac{1}{2} x^{3} + 2 d x

\frac{17}{8}

Solution steps

\int_{0}^{1} \frac{1}{2} x^{3} + 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}^{1} \frac{1}{2} x^{3} d x + \int_{0}^{1} 2 d x

\int_{0}^{1} \frac{1}{2} x^{3} d x = \frac{1}{8}

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

= \frac{1}{8} + 2

Simplify

\frac{1}{8} + 2 : \frac{17}{8}

= \frac{17}{8}

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What is the integral from 0 to 1 of 1/2 x^3+2 ?
The integral from 0 to 1 of 1/2 x^3+2 is 17/8