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

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

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

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

- \frac{9}{2}

Decimal

- 4.5

Solution steps

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

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

\int_{1}^{4} x d x = \frac{15}{2}

= 3 - \frac{15}{2}

Simplify

3 - \frac{15}{2} : - \frac{9}{2}

= - \frac{9}{2}

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