What is the integral from 3 to 4 of x+1/3 x^3 ?

The integral from 3 to 4 of x+1/3 x^3 is 217/12

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integral from 3 to 4 of x+1/3 x^3

\int_{3}^{4} x + \frac{1}{3} x^{3} d x

\frac{217}{12}

Solution steps

\int_{3}^{4} x + \frac{1}{3} x^{3} 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_{3}^{4} x d x + \int_{3}^{4} \frac{1}{3} x^{3} d x

\int_{3}^{4} x d x = \frac{7}{2}

\int_{3}^{4} \frac{1}{3} x^{3} d x = \frac{175}{12}

= \frac{7}{2} + \frac{175}{12}

Simplify

\frac{7}{2} + \frac{175}{12} : \frac{217}{12}

= \frac{217}{12}

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What is the integral from 3 to 4 of x+1/3 x^3 ?
The integral from 3 to 4 of x+1/3 x^3 is 217/12