What is the integral from 0 to b of (7x)/8 ?

The integral from 0 to b of (7x)/8 is (7b^2)/(16)

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integral from 0 to b of (7x)/8

\int_{0}^{b} \frac{7 x}{8} d x

\frac{7 b ^{2}}{16}

Solution steps

\int_{0}^{b} \frac{7 x}{8} d x

Take the constant out:

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

= \frac{7}{8} \cdot \int_{0}^{b} x d x

Apply the Power Rule

= \frac{7}{8} [\frac{x ^{2}}{2}]_{0}^{b}

Compute the boundaries:

\frac{b ^{2}}{2}

= \frac{7}{8} \cdot \frac{b ^{2}}{2}

Simplify

= \frac{7 b ^{2}}{16}

What is the integral from 0 to b of (7x)/8 ?
The integral from 0 to b of (7x)/8 is (7b^2)/(16)