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

The integral from 1 to 4 of (x+2-x^2) is -15/2

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

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

- \frac{15}{2}

Decimal

- 7.5

Solution steps

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

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

\int_{1}^{4} 2 d x = 6

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

= \frac{15}{2} + 6 - 21

Simplify

\frac{15}{2} + 6 - 21 : - \frac{15}{2}

= - \frac{15}{2}

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What is the integral from 1 to 4 of (x+2-x^2) ?
The integral from 1 to 4 of (x+2-x^2) is -15/2