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

The integral from 1 to 4 of (x^2-5x+4) is -9/2

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

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

- \frac{9}{2}

Decimal

- 4.5

Solution steps

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

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 5 x d x = \frac{75}{2}

\int_{1}^{4} 4 d x = 12

= 21 - \frac{75}{2} + 12

Simplify

21 - \frac{75}{2} + 12 : - \frac{9}{2}

= - \frac{9}{2}

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What is the integral from 1 to 4 of (x^2-5x+4) ?
The integral from 1 to 4 of (x^2-5x+4) is -9/2