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

The integral from 0 to 1 of pi(sqrt(y))^2 is pi/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of pi(sqrt(y))^2

\int_{0}^{1} π (y)^{2} d y

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{1} π (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}^{1} (y)^{2} d y

Simplify

(y)^{2} : y

= π \cdot \int_{0}^{1} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{1}

= π [\frac{y ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= π \frac{1}{2}

Simplify

= \frac{π}{2}

\int_{0}^{x} \frac{6}{1 + 6 x ^{2}} d x

\int_{0}^{2} 3 x - 1 d x

\int_{0}^{4} 5 x^{2} + 3 x + 1 d x

\int_{0}^{8} (x^{2} - 5) d x

\int_{\frac{π}{2}}^{π} 0 d x

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