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

The integral from 1 to 9 of (1+sqrt(x)) is 76/3

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

\int_{1}^{9} (1 + x) d x

\frac{76}{3}

Decimal Notation

25.33333 \dots

Solution steps

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

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

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

= 8 + \frac{52}{3}

Simplify

8 + \frac{52}{3} : \frac{76}{3}

= \frac{76}{3}

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What is the integral from 1 to 9 of (1+sqrt(x)) ?
The integral from 1 to 9 of (1+sqrt(x)) is 76/3