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

The integral from 0 to 1 of pi(2x)^2 is (4pi)/3

Popular >

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

\int_{0}^{1} π (2 x)^{2} d x

\frac{4 π}{3}

Decimal Notation

4.18879 \dots

Solution steps

\int_{0}^{1} π (2 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}^{1} (2 x)^{2} d x

Simplify

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

= π \cdot \int_{0}^{1} 4 x^{2} d x

Take the constant out:

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

= π 4 \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

= π 4 [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= π 4 \cdot \frac{1}{3}

Simplify

= \frac{4 π}{3}

\int \frac{2 s - 8}{( s ^{2} - 8 s + 25 ) ^{2}} d s

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

\frac{d y}{d x} - y = e^{x} \cdot y^{2}

\int_{4}^{\infty} 5 e^{- \frac{y}{2}} d y

\int \frac{x}{x + 2 y} d x

What is the integral from 0 to 1 of pi(2x)^2 ?
The integral from 0 to 1 of pi(2x)^2 is (4pi)/3