What is the integral from 0 to 4 of (5x^2+sqrt(x)) ?

The integral from 0 to 4 of (5x^2+sqrt(x)) is 112

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integral from 0 to 4 of (5x^2+sqrt(x))

\int_{0}^{4} (5 x^{2} + x) d x

112

Solution steps

\int_{0}^{4} 5 x^{2} + 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

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

\int_{0}^{4} 5 x^{2} d x = \frac{320}{3}

\int_{0}^{4} x d x = \frac{16}{3}

= \frac{320}{3} + \frac{16}{3}

Simplify

\frac{320}{3} + \frac{16}{3} : 112

= 112

What is the integral from 0 to 4 of (5x^2+sqrt(x)) ?
The integral from 0 to 4 of (5x^2+sqrt(x)) is 112