What is the integral from 2 to 10 of (x^3+7x)/2 ?

The integral from 2 to 10 of (x^3+7x)/2 is 1416

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integral from 2 to 10 of (x^3+7x)/2

\int_{2}^{10} \frac{x ^{3} + 7 x}{2} d x

1416

Solution steps

\int_{2}^{10} \frac{x ^{3} + 7 x}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{2}^{10} x^{3} + 7 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

= \frac{1}{2} (\int_{2}^{10} x^{3} d x + \int_{2}^{10} 7 x d x)

\int_{2}^{10} x^{3} d x = 2496

\int_{2}^{10} 7 x d x = 336

= \frac{1}{2} (2496 + 336)

Simplify

\frac{1}{2} (2496 + 336) : 1416

= 1416

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What is the integral from 2 to 10 of (x^3+7x)/2 ?
The integral from 2 to 10 of (x^3+7x)/2 is 1416