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

The integral from 0 to 1 of x^3+2x^2-3x is -7/12

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

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

- \frac{7}{12}

Decimal

- 0.58333 \dots

Solution steps

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

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

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

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

= \frac{1}{4} + \frac{2}{3} - \frac{3}{2}

Simplify

\frac{1}{4} + \frac{2}{3} - \frac{3}{2} : - \frac{7}{12}

= - \frac{7}{12}

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What is the integral from 0 to 1 of x^3+2x^2-3x ?
The integral from 0 to 1 of x^3+2x^2-3x is -7/12