What is the integral from 0 to 100 of 2((x^2)-ax) ?

The integral from 0 to 100 of 2((x^2)-ax) is 2(1000000/3-a*5000)

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integral from 0 to 100 of 2((x^2)-ax)

\int_{0}^{100} 2 ((x^{2}) - a x) d x

2 (\frac{1000000}{3} - a \cdot 5000)

Solution steps

\int_{0}^{100} 2 (x^{2} - a x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{100} x^{2} - a x 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

= 2 (\int_{0}^{100} x^{2} d x - \int_{0}^{100} a x d x)

\int_{0}^{100} x^{2} d x = \frac{1000000}{3}

\int_{0}^{100} a x d x = a \cdot 5000

= 2 (\frac{1000000}{3} - a \cdot 5000)

What is the integral from 0 to 100 of 2((x^2)-ax) ?
The integral from 0 to 100 of 2((x^2)-ax) is 2(1000000/3-a*5000)