What is the integral from 0 to 3 of (x^2-3x+2) ?

The integral from 0 to 3 of (x^2-3x+2) is 3/2

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integral from 0 to 3 of (x^2-3x+2)

\int_{0}^{3} (x^{2} - 3 x + 2) d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{0}^{3} x^{2} - 3 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_{0}^{3} x^{2} d x - \int_{0}^{3} 3 x d x + \int_{0}^{3} 2 d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 3 x d x = \frac{27}{2}

\int_{0}^{3} 2 d x = 6

= 9 - \frac{27}{2} + 6

Simplify

9 - \frac{27}{2} + 6 : \frac{3}{2}

= \frac{3}{2}

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What is the integral from 0 to 3 of (x^2-3x+2) ?
The integral from 0 to 3 of (x^2-3x+2) is 3/2