What is the integral from-6 to 6 of 1/2 (36-x^2) ?

The integral from-6 to 6 of 1/2 (36-x^2) is 144

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integral from-6 to 6 of 1/2 (36-x^2)

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

144

Solution steps

\int_{- 6}^{6} \frac{1}{2} (36 - x^{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

\int_{- π}^{π} sin (2 x) sin (3 x) d x

f (x) = e^{x^{5}}

\int \frac{10}{10 + e ^{x}} d x

\frac{d}{d x} (\frac{( x + y )}{( x - y )})

x \to 0 lim (- 3 - 2 x)

What is the integral from-6 to 6 of 1/2 (36-x^2) ?
The integral from-6 to 6 of 1/2 (36-x^2) is 144