What is the integral from 0 to 1 of-x^3-x^2+2x ?

The integral from 0 to 1 of-x^3-x^2+2x is 5/12

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integral from 0 to 1 of-x^3-x^2+2x

\int_{0}^{1} - x^{3} - x^{2} + 2 x d x

\frac{5}{12}

Decimal

0.41666 \dots

Solution steps

\int_{0}^{1} - x^{3} - x^{2} + 2 x 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}^{1} x^{3} d x - \int_{0}^{1} x^{2} d x + \int_{0}^{1} 2 x d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 2 x d x = 1

= - \frac{1}{4} - \frac{1}{3} + 1

Simplify

- \frac{1}{4} - \frac{1}{3} + 1 : \frac{5}{12}

= \frac{5}{12}

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What is the integral from 0 to 1 of-x^3-x^2+2x ?
The integral from 0 to 1 of-x^3-x^2+2x is 5/12