What is the integral from-6 to 6 of ((36-x^2))/2 ?

The integral from-6 to 6 of ((36-x^2))/2 is 144

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integral from-6 to 6 of ((36-x^2))/2

\int_{- 6}^{6} \frac{( 36 - x ^{2} )}{2} d x

144

Solution steps

\int_{- 6}^{6} \frac{36 - x ^{2}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{- 6}^{6} 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}{2} (\int_{- 6}^{6} 36 d x - \int_{- 6}^{6} x^{2} d x)

\int_{- 6}^{6} 36 d x = 432

\int_{- 6}^{6} x^{2} d x = 144

= \frac{1}{2} (432 - 144)

Simplify

\frac{1}{2} (432 - 144) : 144

= 144

What is the integral from-6 to 6 of ((36-x^2))/2 ?
The integral from-6 to 6 of ((36-x^2))/2 is 144