What is the integral from 1 to 2 of x^3-2x^2-5x+6 ?

The integral from 1 to 2 of x^3-2x^2-5x+6 is -29/12

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integral from 1 to 2 of x^3-2x^2-5x+6

\int_{1}^{2} x^{3} - 2 x^{2} - 5 x + 6 d x

- \frac{29}{12}

Decimal

- 2.41666 \dots

Solution steps

\int_{1}^{2} x^{3} - 2 x^{2} - 5 x + 6 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} 2 x^{2} d x - \int_{1}^{2} 5 x d x + \int_{1}^{2} 6 d x

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

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

\int_{1}^{2} 5 x d x = \frac{15}{2}

\int_{1}^{2} 6 d x = 6

= \frac{15}{4} - \frac{14}{3} - \frac{15}{2} + 6

Simplify

\frac{15}{4} - \frac{14}{3} - \frac{15}{2} + 6 : - \frac{29}{12}

= - \frac{29}{12}

What is the integral from 1 to 2 of x^3-2x^2-5x+6 ?
The integral from 1 to 2 of x^3-2x^2-5x+6 is -29/12