What is the integral from 0 to 1 of pi(x^3)^2 ?

The integral from 0 to 1 of pi(x^3)^2 is pi/7

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integral from 0 to 1 of pi(x^3)^2

\int_{0}^{1} π (x^{3})^{2} d x

\frac{π}{7}

Decimal

0.44879 \dots

Solution steps

\int_{0}^{1} π (x^{3})^{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^{3})^{2} d x

Simplify

(x^{3})^{2} : x^{6}

= π \cdot \int_{0}^{1} x^{6} d x

Apply the Power Rule

: [\frac{x ^{7}}{7}]_{0}^{1}

= π [\frac{x ^{7}}{7}]_{0}^{1}

Compute the boundaries:

\frac{1}{7}

= π \frac{1}{7}

Simplify

= \frac{π}{7}

\int y e^{- x^{2}} d x

(- 5, - 3), (5, 2)

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

n = 1 \sum \infty n^{2} \cdot x^{n}

4 2 x^{12} + sin (4 x)

What is the integral from 0 to 1 of pi(x^3)^2 ?
The integral from 0 to 1 of pi(x^3)^2 is pi/7