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

The integral from 2 to 3 of-x^2+2x+3 is 5/3

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

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

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

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

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 2 x d x = 5

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

= - \frac{19}{3} + 5 + 3

Simplify

- \frac{19}{3} + 5 + 3 : \frac{5}{3}

= \frac{5}{3}

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What is the integral from 2 to 3 of-x^2+2x+3 ?
The integral from 2 to 3 of-x^2+2x+3 is 5/3