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

The integral from 1 to 4 of (4sqrt(x)-x) is 67/6

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

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

\frac{67}{6}

Decimal Notation

11.16666 \dots

Solution steps

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

\int_{1}^{4} 4 x d x = \frac{56}{3}

\int_{1}^{4} x d x = \frac{15}{2}

= \frac{56}{3} - \frac{15}{2}

Simplify

\frac{56}{3} - \frac{15}{2} : \frac{67}{6}

= \frac{67}{6}

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What is the integral from 1 to 4 of (4sqrt(x)-x) ?
The integral from 1 to 4 of (4sqrt(x)-x) is 67/6