What is the integral from-1 to 3 of 2x^2-4x-6 ?

The integral from-1 to 3 of 2x^2-4x-6 is -64/3

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integral from-1 to 3 of 2x^2-4x-6

\int_{- 1}^{3} 2 x^{2} - 4 x - 6 d x

- \frac{64}{3}

Decimal

- 21.33333 \dots

Solution steps

\int_{- 1}^{3} 2 x^{2} - 4 x - 6 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}^{3} 2 x^{2} d x - \int_{- 1}^{3} 4 x d x - \int_{- 1}^{3} 6 d x

\int_{- 1}^{3} 2 x^{2} d x = \frac{56}{3}

\int_{- 1}^{3} 4 x d x = 16

\int_{- 1}^{3} 6 d x = 24

= \frac{56}{3} - 16 - 24

Simplify

\frac{56}{3} - 16 - 24 : - \frac{64}{3}

= - \frac{64}{3}

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What is the integral from-1 to 3 of 2x^2-4x-6 ?
The integral from-1 to 3 of 2x^2-4x-6 is -64/3