What is the integral from-2 to 3 of sqrt(x+6)-x ?

The integral from-2 to 3 of sqrt(x+6)-x is 61/6

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integral from-2 to 3 of sqrt(x+6)-x

\int_{- 2}^{3} x + 6 - x d x

\frac{61}{6}

Decimal

10.16666 \dots

Solution steps

\int_{- 2}^{3} x + 6 - 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_{- 2}^{3} x + 6 d x - \int_{- 2}^{3} x d x

\int_{- 2}^{3} x + 6 d x = \frac{38}{3}

\int_{- 2}^{3} x d x = \frac{5}{2}

= \frac{38}{3} - \frac{5}{2}

Simplify

\frac{38}{3} - \frac{5}{2} : \frac{61}{6}

= \frac{61}{6}

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What is the integral from-2 to 3 of sqrt(x+6)-x ?
The integral from-2 to 3 of sqrt(x+6)-x is 61/6