What is the integral from 0 to 4 of x-2sqrt(x) ?

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

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integral from 0 to 4 of x-2sqrt(x)

\int_{0}^{4} x - 2 x d x

- \frac{8}{3}

Decimal

- 2.66666 \dots

Solution steps

\int_{0}^{4} 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} x d x - \int_{0}^{4} 2 x d x

\int_{0}^{4} x d x = 8

\int_{0}^{4} 2 x d x = \frac{32}{3}

= 8 - \frac{32}{3}

Simplify

8 - \frac{32}{3} : - \frac{8}{3}

= - \frac{8}{3}

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