What is the integral from 4 to 16 of sqrt(x)-1 ?

The integral from 4 to 16 of sqrt(x)-1 is 76/3

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integral from 4 to 16 of sqrt(x)-1

\int_{4}^{16} x - 1 d x

\frac{76}{3}

Decimal Notation

25.33333 \dots

Solution steps

\int_{4}^{16} x - 1 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_{4}^{16} x d x - \int_{4}^{16} 1 d x

\int_{4}^{16} x d x = \frac{112}{3}

\int_{4}^{16} 1 d x = 12

= \frac{112}{3} - 12

Simplify

\frac{112}{3} - 12 : \frac{76}{3}

= \frac{76}{3}

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What is the integral from 4 to 16 of sqrt(x)-1 ?
The integral from 4 to 16 of sqrt(x)-1 is 76/3