What is the integral from 0 to 2-x of 3/4 x ?

The integral from 0 to 2-x of 3/4 x is (3(-x+2)^2)/8

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integral from 0 to 2-x of 3/4 x

\int_{0}^{2 - x} \frac{3}{4} x d x

\frac{3 ( - x + 2 ) ^{2}}{8}

Solution steps

\int_{0}^{2 - x} \frac{3}{4} x d x

Take the constant out:

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

= \frac{3}{4} \cdot \int_{0}^{2 - x} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{2 - x}

= \frac{3}{4} [\frac{x ^{2}}{2}]_{0}^{2 - x}

Compute the boundaries:

\frac{1}{2} (- x + 2)^{2}

= \frac{3}{4} \cdot \frac{1}{2} (- x + 2)^{2}

Simplify

= \frac{3 ( - x + 2 ) ^{2}}{8}

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What is the integral from 0 to 2-x of 3/4 x ?
The integral from 0 to 2-x of 3/4 x is (3(-x+2)^2)/8