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

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

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

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

\frac{3 x ^{2}}{4} - \frac{x ^{3}}{4}

Solution steps

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

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

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

= \frac{3 x ^{2}}{4} - \frac{x ^{3}}{4}

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