What is the integral from 1 to 5 of (2x^2-12x+10) ?

The integral from 1 to 5 of (2x^2-12x+10) is -64/3

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integral from 1 to 5 of (2x^2-12x+10)

\int_{1}^{5} (2 x^{2} - 12 x + 10) d x

- \frac{64}{3}

Decimal

- 21.33333 \dots

Solution steps

\int_{1}^{5} 2 x^{2} - 12 x + 10 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}^{5} 2 x^{2} d x - \int_{1}^{5} 12 x d x + \int_{1}^{5} 10 d x

\int_{1}^{5} 2 x^{2} d x = \frac{248}{3}

\int_{1}^{5} 12 x d x = 144

\int_{1}^{5} 10 d x = 40

= \frac{248}{3} - 144 + 40

Simplify

\frac{248}{3} - 144 + 40 : - \frac{64}{3}

= - \frac{64}{3}

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What is the integral from 1 to 5 of (2x^2-12x+10) ?
The integral from 1 to 5 of (2x^2-12x+10) is -64/3