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

The integral from 1 to 4 of (x-sqrt(x)) is 17/6

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

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

\frac{17}{6}

Decimal

2.83333 \dots

Solution steps

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

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

\int_{1}^{4} x d x = \frac{14}{3}

= \frac{15}{2} - \frac{14}{3}

Simplify

\frac{15}{2} - \frac{14}{3} : \frac{17}{6}

= \frac{17}{6}

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What is the integral from 1 to 4 of (x-sqrt(x)) ?
The integral from 1 to 4 of (x-sqrt(x)) is 17/6