What is the integral from 0 to 1 of pi(x^2)^2 ?

The integral from 0 to 1 of pi(x^2)^2 is pi/5

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integral from 0 to 1 of pi(x^2)^2

\int_{0}^{1} π (x^{2})^{2} d x

\frac{π}{5}

Decimal Notation

0.62831 \dots

Solution steps

\int_{0}^{1} π (x^{2})^{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}^{1} (x^{2})^{2} d x

Simplify

(x^{2})^{2} : x^{4}

= π \cdot \int_{0}^{1} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{1}

= π [\frac{x ^{5}}{5}]_{0}^{1}

Compute the boundaries:

\frac{1}{5}

= π \frac{1}{5}

Simplify

= \frac{π}{5}

\frac{d}{d t} (6 t)

f (x) = \frac{x}{x + 6}, at x = 1

f (x) = 3 sec (x), - \frac{π}{6} \leq x \leq \frac{π}{6}

\frac{d y}{d x} = \frac{( x - 3 )}{y + 1}

\frac{\partial}{\partial y} (x e^{\frac{y}{z}})

What is the integral from 0 to 1 of pi(x^2)^2 ?
The integral from 0 to 1 of pi(x^2)^2 is pi/5