What is the integral from 0 to 1 of (4sqrt(x))-(4x) ?

The integral from 0 to 1 of (4sqrt(x))-(4x) is 2/3

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integral from 0 to 1 of (4sqrt(x))-(4x)

\int_{0}^{1} (4 x) - (4 x) d x

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{0}^{1} 4 x - 4 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}^{1} 4 x d x - \int_{0}^{1} 4 x d x

\int_{0}^{1} 4 x d x = \frac{8}{3}

\int_{0}^{1} 4 x d x = 2

= \frac{8}{3} - 2

Simplify

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

= \frac{2}{3}

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What is the integral from 0 to 1 of (4sqrt(x))-(4x) ?
The integral from 0 to 1 of (4sqrt(x))-(4x) is 2/3