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

The integral from 1 to 3 of x^3-2x^2-5x+6 is -16/3

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

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

- \frac{16}{3}

Decimal Notation

- 5.33333 \dots

Solution steps

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

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 5 x d x = 20

\int_{1}^{3} 6 d x = 12

= 20 - \frac{52}{3} - 20 + 12

Simplify

20 - \frac{52}{3} - 20 + 12 : - \frac{16}{3}

= - \frac{16}{3}

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What is the integral from 1 to 3 of x^3-2x^2-5x+6 ?
The integral from 1 to 3 of x^3-2x^2-5x+6 is -16/3