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

The integral from 1 to 2 of 2x^2-x^3 is 11/12

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

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

\frac{11}{12}

Decimal

0.91666 \dots

Solution steps

\int_{1}^{2} 2 x^{2} - x^{3} 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_{1}^{2} 2 x^{2} d x - \int_{1}^{2} x^{3} d x

\int_{1}^{2} 2 x^{2} d x = \frac{14}{3}

\int_{1}^{2} x^{3} d x = \frac{15}{4}

= \frac{14}{3} - \frac{15}{4}

Simplify

\frac{14}{3} - \frac{15}{4} : \frac{11}{12}

= \frac{11}{12}

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What is the integral from 1 to 2 of 2x^2-x^3 ?
The integral from 1 to 2 of 2x^2-x^3 is 11/12