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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\int_{1}^{4} \frac{1}{2 x} d x

1

Solution steps

\int_{1}^{4} \frac{1}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{4} \frac{1}{x} d x

Apply the Power Rule

= \frac{1}{2} [2 x^{\frac{1}{2}}]_{1}^{4}

Apply radical rule:

= \frac{1}{2} [2 x]_{1}^{4}

Compute the boundaries:

2

= \frac{1}{2} \cdot 2

Simplify

= 1

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