What is the integral from 0 to 2 of 9375(4-x^2) ?

The integral from 0 to 2 of 9375(4-x^2) is 50000

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integral from 0 to 2 of 9375(4-x^2)

\int_{0}^{2} 9375 (4 - x^{2}) d x

50000

Solution steps

\int_{0}^{2} 9375 (4 - x^{2}) d x

Take the constant out:

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

= 9375 \cdot \int_{0}^{2} 4 - x^{2} 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

= 9375 (\int_{0}^{2} 4 d x - \int_{0}^{2} x^{2} d x)

\int_{0}^{2} 4 d x = 8

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

= 9375 (8 - \frac{8}{3})

Simplify

9375 (8 - \frac{8}{3}) : 50000

= 50000

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What is the integral from 0 to 2 of 9375(4-x^2) ?
The integral from 0 to 2 of 9375(4-x^2) is 50000