What is the integral from-2 to 3 of (5+x-6x^2) ?

The integral from-2 to 3 of (5+x-6x^2) is -85/2

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integral from-2 to 3 of (5+x-6x^2)

\int_{- 2}^{3} (5 + x - 6 x^{2}) d x

- \frac{85}{2}

Decimal

- 42.5

Solution steps

\int_{- 2}^{3} 5 + x - 6 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_{- 2}^{3} 5 d x + \int_{- 2}^{3} x d x - \int_{- 2}^{3} 6 x^{2} d x

\int_{- 2}^{3} 5 d x = 25

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

\int_{- 2}^{3} 6 x^{2} d x = 70

= 25 + \frac{5}{2} - 70

Simplify

25 + \frac{5}{2} - 70 : - \frac{85}{2}

= - \frac{85}{2}

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What is the integral from-2 to 3 of (5+x-6x^2) ?
The integral from-2 to 3 of (5+x-6x^2) is -85/2