What is the integral from 0 to 5 of (x+1)/2 ?

The integral from 0 to 5 of (x+1)/2 is 35/4

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integral from 0 to 5 of (x+1)/2

\int_{0}^{5} \frac{x + 1}{2} d x

\frac{35}{4}

Decimal

8.75

Solution steps

\int_{0}^{5} \frac{x + 1}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{5} 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

= \frac{1}{2} (\int_{0}^{5} x d x + \int_{0}^{5} 1 d x)

\int_{0}^{5} x d x = \frac{25}{2}

\int_{0}^{5} 1 d x = 5

= \frac{1}{2} (\frac{25}{2} + 5)

Simplify

\frac{1}{2} (\frac{25}{2} + 5) : \frac{35}{4}

= \frac{35}{4}

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What is the integral from 0 to 5 of (x+1)/2 ?
The integral from 0 to 5 of (x+1)/2 is 35/4