What is the integral from 1 to 9 of sqrt(x)-1 ?

The integral from 1 to 9 of sqrt(x)-1 is 28/3

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integral from 1 to 9 of sqrt(x)-1

\int_{1}^{9} x - 1 d x

\frac{28}{3}

Decimal

9.33333 \dots

Solution steps

\int_{1}^{9} 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_{1}^{9} x d x - \int_{1}^{9} 1 d x

\int_{1}^{9} x d x = \frac{52}{3}

\int_{1}^{9} 1 d x = 8

= \frac{52}{3} - 8

Simplify

\frac{52}{3} - 8 : \frac{28}{3}

= \frac{28}{3}

What is the integral from 1 to 9 of sqrt(x)-1 ?
The integral from 1 to 9 of sqrt(x)-1 is 28/3