What is the integral from 0 to x of ((36-x^2))/(144) ?

The integral from 0 to x of ((36-x^2))/(144) is 1/144 (36x-(x^3)/3)

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integral from 0 to x of ((36-x^2))/(144)

\int_{0}^{x} \frac{( 36 - x ^{2} )}{144} d x

\frac{1}{144} (36 x - \frac{x ^{3}}{3})

Solution steps

\int_{0}^{x} \frac{36 - x ^{2}}{144} d x

Take the constant out:

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

= \frac{1}{144} \cdot \int_{0}^{x} 36 - 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

= \frac{1}{144} (\int_{0}^{x} 36 d x - \int_{0}^{x} x^{2} d x)

\int_{0}^{x} 36 d x = 36 x

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

= \frac{1}{144} (36 x - \frac{x ^{3}}{3})

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What is the integral from 0 to x of ((36-x^2))/(144) ?
The integral from 0 to x of ((36-x^2))/(144) is 1/144 (36x-(x^3)/3)