What is the integral from 0 to 8 of 2x^2-24x+70 ?

The integral from 0 to 8 of 2x^2-24x+70 is 400/3

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integral from 0 to 8 of 2x^2-24x+70

\int_{0}^{8} 2 x^{2} - 24 x + 70 d x

\frac{400}{3}

Decimal Notation

133.33333 \dots

Solution steps

\int_{0}^{8} 2 x^{2} - 24 x + 70 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_{0}^{8} 2 x^{2} d x - \int_{0}^{8} 24 x d x + \int_{0}^{8} 70 d x

\int_{0}^{8} 2 x^{2} d x = \frac{1024}{3}

\int_{0}^{8} 24 x d x = 768

\int_{0}^{8} 70 d x = 560

= \frac{1024}{3} - 768 + 560

Simplify

\frac{1024}{3} - 768 + 560 : \frac{400}{3}

= \frac{400}{3}

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What is the integral from 0 to 8 of 2x^2-24x+70 ?
The integral from 0 to 8 of 2x^2-24x+70 is 400/3