What is the integral from 9 to 16 of (sqrt(x)-4) ?

The integral from 9 to 16 of (sqrt(x)-4) is -10/3

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integral from 9 to 16 of (sqrt(x)-4)

\int_{9}^{16} (x - 4) d x

- \frac{10}{3}

Decimal

- 3.33333 \dots

Solution steps

\int_{9}^{16} x - 4 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} 4 d x

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

\int_{9}^{16} 4 d x = 28

= \frac{74}{3} - 28

Simplify

\frac{74}{3} - 28 : - \frac{10}{3}

= - \frac{10}{3}

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What is the integral from 9 to 16 of (sqrt(x)-4) ?
The integral from 9 to 16 of (sqrt(x)-4) is -10/3