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

The integral from-2 to 3 of (x^2+3x-1) is 85/6

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

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

\frac{85}{6}

Decimal

14.16666 \dots

Solution steps

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

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

\int_{- 2}^{3} 3 x d x = \frac{15}{2}

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

= \frac{35}{3} + \frac{15}{2} - 5

Simplify

\frac{35}{3} + \frac{15}{2} - 5 : \frac{85}{6}

= \frac{85}{6}

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What is the integral from-2 to 3 of (x^2+3x-1) ?
The integral from-2 to 3 of (x^2+3x-1) is 85/6