What is the integral from 0 to 6 of ((36-x^2))/(144) ?

The integral from 0 to 6 of ((36-x^2))/(144) is 1

Popular >

integral from 0 to 6 of ((36-x^2))/(144)

\int_{0}^{6} \frac{( 36 - x ^{2} )}{144} d x

1

Solution steps

\int_{0}^{6} \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}^{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}{144} (\int_{0}^{6} 36 d x - \int_{0}^{6} x^{2} d x)

\int_{0}^{6} 36 d x = 216

\int_{0}^{6} x^{2} d x = 72

= \frac{1}{144} (216 - 72)

Simplify

\frac{1}{144} (216 - 72) : 1

= 1

\int_{2}^{3} \frac{x}{1 + x} d x

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

\int_{0}^{1} 10 0^{x} d x

\int_{0}^{1} e^{3 + 3 y} - e^{3 y} d y

\int_{0}^{\frac{π}{2}} x sin (x^{2}) d x

What is the integral from 0 to 6 of ((36-x^2))/(144) ?
The integral from 0 to 6 of ((36-x^2))/(144) is 1