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

The integral from-1 to 1 of (x^2-3x+3) is 20/3

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

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

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

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

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

\int_{- 1}^{1} 3 x d x = 0

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

= \frac{2}{3} - 0 + 6

Simplify

\frac{2}{3} - 0 + 6 : \frac{20}{3}

= \frac{20}{3}

\int_{1}^{5} 2 x^{3} d x

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\int_{1}^{8} 2 lo g_{4} (x + 3) d x

\int_{1}^{2} 2 x^{2} - x^{3} d x

What is the integral from-1 to 1 of (x^2-3x+3) ?
The integral from-1 to 1 of (x^2-3x+3) is 20/3