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

The integral from 1 to 2 of-x^3+3x^2-2x is 1/4

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

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

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

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

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

= - \frac{15}{4} + 7 - 3

Simplify

- \frac{15}{4} + 7 - 3 : \frac{1}{4}

= \frac{1}{4}

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\int_{2}^{18} 4 x^{3} - 2 x + 2 d x

What is the integral from 1 to 2 of-x^3+3x^2-2x ?
The integral from 1 to 2 of-x^3+3x^2-2x is 1/4