What is the integral from 1 to 3 of (x^2-4x+5) ?

The integral from 1 to 3 of (x^2-4x+5) is 8/3

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integral from 1 to 3 of (x^2-4x+5)

\int_{1}^{3} (x^{2} - 4 x + 5) d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{1}^{3} x^{2} - 4 x + 5 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} 4 x d x + \int_{1}^{3} 5 d x

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

\int_{1}^{3} 4 x d x = 16

\int_{1}^{3} 5 d x = 10

= \frac{26}{3} - 16 + 10

Simplify

\frac{26}{3} - 16 + 10 : \frac{8}{3}

= \frac{8}{3}

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What is the integral from 1 to 3 of (x^2-4x+5) ?
The integral from 1 to 3 of (x^2-4x+5) is 8/3