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

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

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

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

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

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

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

\int_{1}^{3} x d x = 4

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

= \frac{26}{3} - 4 + 2

Simplify

\frac{26}{3} - 4 + 2 : \frac{20}{3}

= \frac{20}{3}

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