What is the integral from 0 to 2 of sqrt(x)-x^2 ?

The integral from 0 to 2 of sqrt(x)-x^2 is (4sqrt(2))/3-8/3

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integral from 0 to 2 of sqrt(x)-x^2

\int_{0}^{2} x - x^{2} d x

\frac{4 2}{3} - \frac{8}{3}

Decimal

- 0.78104 \dots

Solution steps

\int_{0}^{2} x - x^{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} x d x - \int_{0}^{2} x^{2} d x

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

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

= \frac{4 2}{3} - \frac{8}{3}

What is the integral from 0 to 2 of sqrt(x)-x^2 ?
The integral from 0 to 2 of sqrt(x)-x^2 is (4sqrt(2))/3-8/3