What is the integral from-1 to 2 of (5x^2+1/3 x-1/2) ?

The integral from-1 to 2 of (5x^2+1/3 x-1/2) is 14

integral from-1 to 2 of (5x^2+1/3 x-1/2)

\int_{- 1}^{2} (5 x^{2} + \frac{1}{3} x - \frac{1}{2}) d x

14

Solution steps

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

\int_{- 1}^{2} 5 x^{2} d x = 15

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

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

= 15 + \frac{1}{2} - \frac{3}{2}

Simplify

15 + \frac{1}{2} - \frac{3}{2} : 14

= 14

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What is the integral from-1 to 2 of (5x^2+1/3 x-1/2) ?
The integral from-1 to 2 of (5x^2+1/3 x-1/2) is 14