What is the integral from 9 to 16 of (sqrt(x)-2) ?

The integral from 9 to 16 of (sqrt(x)-2) is 32/3

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integral from 9 to 16 of (sqrt(x)-2)

\int_{9}^{16} (x - 2) d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

\int_{9}^{16} x - 2 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_{9}^{16} x d x - \int_{9}^{16} 2 d x

\int_{9}^{16} x d x = \frac{74}{3}

\int_{9}^{16} 2 d x = 14

= \frac{74}{3} - 14

Simplify

\frac{74}{3} - 14 : \frac{32}{3}

= \frac{32}{3}

What is the integral from 9 to 16 of (sqrt(x)-2) ?
The integral from 9 to 16 of (sqrt(x)-2) is 32/3