What is the integral from 0 to 4 of pix^2 ?

The integral from 0 to 4 of pix^2 is (64pi)/3

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integral from 0 to 4 of pix^2

\int_{0}^{4} π x^{2} d x

\frac{64 π}{3}

Decimal Notation

67.02064 \dots

Solution steps

\int_{0}^{4} π x^{2} d x

Take the constant out:

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

= π \cdot \int_{0}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{4}

= π [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= π \frac{64}{3}

Simplify

= \frac{64 π}{3}

- 5 e^{- \frac{x}{3}} + 2

x \to - 4 lim (\frac{x - 4}{x - 8})

x \to \infty lim (arcsin (\frac{2 x}{5 + 4 x}))

\frac{\partial}{\partial x} (e^{4 x y} \cdot 4 y)

x^{2} y^{^{'}} + 2 x y = 5 y^{3}

What is the integral from 0 to 4 of pix^2 ?
The integral from 0 to 4 of pix^2 is (64pi)/3