What is the integral from 0 to 4 of pi(2sqrt(x))^2 ?

The integral from 0 to 4 of pi(2sqrt(x))^2 is pi32

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 4 of pi(2sqrt(x))^2

\int_{0}^{4} π (2 x)^{2} d x

π 32

Decimal

100.53096 \dots

Solution steps

\int_{0}^{4} 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}^{4} (2 x)^{2} d x

Apply Integration By Parts

: [4 x^{2} - \int 4 x d x]_{0}^{4}

= π [4 x^{2} - \int 4 x d x]_{0}^{4}

\int 4 x d x = 2 x^{2}

= π [4 x^{2} - 2 x^{2}]_{0}^{4}

Simplify

= π [2 x^{2}]_{0}^{4}

Compute the boundaries:

32

= π 32

\int_{0}^{4} 8 + 7 x d x

\int_{- 3}^{0} g (t) d t

\int_{0}^{0.4} x^{2} d x

\int_{0}^{1} 7 x^{3} d x

\int_{0}^{1} 9 x (x^{2} - 1)^{7} d x

What is the integral from 0 to 4 of pi(2sqrt(x))^2 ?
The integral from 0 to 4 of pi(2sqrt(x))^2 is pi32