What is the integral from 0 to 9 of pi(2sqrt(3y))^2 ?

The integral from 0 to 9 of pi(2sqrt(3y))^2 is pi486

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 9 of pi(2sqrt(3y))^2

\int_{0}^{9} π (2 3 y)^{2} d y

π 486

Decimal Notation

1526.81402 \dots

Solution steps

\int_{0}^{9} π (2 3 y)^{2} d y

Take the constant out:

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

= π \cdot \int_{0}^{9} (2 3 y)^{2} d y

Apply Integration By Parts

: [12 y^{2} - \int 12 y d y]_{0}^{9}

= π [12 y^{2} - \int 12 y d y]_{0}^{9}

\int 12 y d y = 6 y^{2}

= π [12 y^{2} - 6 y^{2}]_{0}^{9}

Simplify

= π [6 y^{2}]_{0}^{9}

Compute the boundaries:

486

= π 486

\frac{d}{d x} (x^{3} + 2 x - 5)

x \to 4 lim (\frac{2 x - 1}{x - 4})

\int 5 x e^{- x} d x

y = (x^{2} + 1)^{2}

x y = - 64, (8, - 8)

What is the integral from 0 to 9 of pi(2sqrt(3y))^2 ?
The integral from 0 to 9 of pi(2sqrt(3y))^2 is pi486