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

The integral from 1 to 2 of (3x^2-2x^3) is -1/2

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

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

- \frac{1}{2}

Decimal

- 0.5

Solution steps

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

\int_{1}^{2} 3 x^{2} d x = 7

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

= 7 - \frac{15}{2}

Simplify

7 - \frac{15}{2} : - \frac{1}{2}

= - \frac{1}{2}

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