What is the integral from 0 to 6 of pi/4 (36-x^2) ?

The integral from 0 to 6 of pi/4 (36-x^2) is 36pi

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integral from 0 to 6 of pi/4 (36-x^2)

\int_{0}^{6} \frac{π}{4} (36 - x^{2}) d x

36 π

Decimal Notation

113.09733 \dots

Solution steps

\int_{0}^{6} \frac{π}{4} (36 - x^{2}) d x

Take the constant out:

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

= \frac{π}{4} \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{π}{4} (\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{π}{4} (216 - 72)

Simplify

\frac{π}{4} (216 - 72) : 36 π

= 36 π

x \to 2 lim (\frac{x}{x - 1})

\frac{2 x}{( 1 - 4 x ) ^{5}}

\int sin (θ) cos^{2} (θ) d θ

x \to 0 + lim (\frac{x + 4}{x})

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

What is the integral from 0 to 6 of pi/4 (36-x^2) ?
The integral from 0 to 6 of pi/4 (36-x^2) is 36pi