What is the integral from 0 to 20 of x^2-17x+70 ?

The integral from 0 to 20 of x^2-17x+70 is 2000/3

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integral from 0 to 20 of x^2-17x+70

\int_{0}^{20} x^{2} - 17 x + 70 d x

\frac{2000}{3}

Decimal

666.66666 \dots

Solution steps

\int_{0}^{20} x^{2} - 17 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}^{20} x^{2} d x - \int_{0}^{20} 17 x d x + \int_{0}^{20} 70 d x

\int_{0}^{20} x^{2} d x = \frac{8000}{3}

\int_{0}^{20} 17 x d x = 3400

\int_{0}^{20} 70 d x = 1400

= \frac{8000}{3} - 3400 + 1400

Simplify

\frac{8000}{3} - 3400 + 1400 : \frac{2000}{3}

= \frac{2000}{3}

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What is the integral from 0 to 20 of x^2-17x+70 ?
The integral from 0 to 20 of x^2-17x+70 is 2000/3