What is the integral from 0 to 1 of 2/(sqrt(x)) ?

The integral from 0 to 1 of 2/(sqrt(x)) is 4

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 2/(sqrt(x))

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

4

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{0}^{1} \frac{1}{x} d x

Apply the Power Rule

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

= 2 [2 x^{\frac{1}{2}}]_{0}^{1}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 [2 x]_{0}^{1}

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

\int_{1}^{4} (10 - x) d x

\int_{0}^{5} 8 d x

\int_{1}^{5} \frac{x}{2 x ^{2} - 1} d x

\int_{- 2}^{- 1} \frac{x}{( x ^{2} + 3 ) ^{2}} d x

\int_{0}^{1} y^{2} 1 - y^{2} d y

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