What is the integral of x/(b-a) ?

The integral of x/(b-a) is (x^2)/(2(b-a))+C

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integral of x/(b-a)

\int \frac{x}{b - a} d x

\frac{x ^{2}}{2 ( b - a )} + C

Solution steps

\int \frac{x}{b - a} d x

Take the constant out:

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

= \frac{1}{b - a} \cdot \int x d x

Apply the Power Rule

= \frac{1}{b - a} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{b - a} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 ( b - a )}

= \frac{x ^{2}}{2 ( b - a )}

Add a constant to the solution

= \frac{x ^{2}}{2 ( b - a )} + C