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

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

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

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

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

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

= \frac{26}{3} - 8 + 6

Simplify

\frac{26}{3} - 8 + 6 : \frac{20}{3}

= \frac{20}{3}

\int_{1}^{3} (\frac{1}{x ^{3}}) d x

\int_{0}^{8} \frac{x}{9 + 2 x} d x

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

\int_{0}^{L} x^{3} d x

\int_{1}^{6} (\frac{x}{6} - \frac{5}{x}) d x

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