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

The integral from-2 to 5 of (x^2-3x+3) is 203/6

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

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

\frac{203}{6}

Decimal

33.83333 \dots

Solution steps

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

\int_{- 2}^{5} x^{2} d x = \frac{133}{3}

\int_{- 2}^{5} 3 x d x = \frac{63}{2}

\int_{- 2}^{5} 3 d x = 21

= \frac{133}{3} - \frac{63}{2} + 21

Simplify

\frac{133}{3} - \frac{63}{2} + 21 : \frac{203}{6}

= \frac{203}{6}

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What is the integral from-2 to 5 of (x^2-3x+3) ?
The integral from-2 to 5 of (x^2-3x+3) is 203/6