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

The integral from 1 to 4 of sqrt(x)-1 is 5/3

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

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

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

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

\int_{1}^{4} x d x = \frac{14}{3}

\int_{1}^{4} 1 d x = 3

= \frac{14}{3} - 3

Simplify

\frac{14}{3} - 3 : \frac{5}{3}

= \frac{5}{3}

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What is the integral from 1 to 4 of sqrt(x)-1 ?
The integral from 1 to 4 of sqrt(x)-1 is 5/3