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

The integral from 1 to 3 of (x^3+2x^2-5x+2) is 64/3

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

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

\frac{64}{3}

Decimal Notation

21.33333 \dots

Solution steps

\int_{1}^{3} x^{3} + 2 x^{2} - 5 x + 2 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} 2 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} 2 d x = 4

= 20 + \frac{52}{3} - 20 + 4

Simplify

20 + \frac{52}{3} - 20 + 4 : \frac{64}{3}

= \frac{64}{3}

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What is the integral from 1 to 3 of (x^3+2x^2-5x+2) ?
The integral from 1 to 3 of (x^3+2x^2-5x+2) is 64/3