What is the integral from a to b of (x-x^2) ?

The integral from a to b of (x-x^2) is (b^2-a^2)/2-(b^3-a^3)/3

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integral from a to b of (x-x^2)

\int_{a}^{b} (x - x^{2}) d x

\frac{b ^{2} - a ^{2}}{2} - \frac{b ^{3} - a ^{3}}{3}

Solution steps

\int_{a}^{b} x - 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_{a}^{b} x d x - \int_{a}^{b} x^{2} d x

\int_{a}^{b} x d x = \frac{b ^{2} - a ^{2}}{2}

\int_{a}^{b} x^{2} d x = \frac{b ^{3} - a ^{3}}{3}

= \frac{b ^{2} - a ^{2}}{2} - \frac{b ^{3} - a ^{3}}{3}

\int_{- 2}^{3} y - (y^{2} - 6) d y

\int_{- 2}^{2} \frac{8}{x ^{2} + 4} d x

\int_{- 1}^{3} - x^{3} - 5 x + 1 d x

\int_{- 1}^{1} (2 x^{2} + 7) d x

\int_{- 1}^{2} 2 x^{3} - 8 x^{2} + 2 x + 12 d x

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