Chapter 9.4, Problem 51E

To determine

Tofind: the value of the integral.

Answer to Problem 51E

The value of integral is $2$ .

Explanation of Solution

Given information:

Theintegral is ${\displaystyle {\int }_0^1\frac{dx}{x^{0.5}}}$ .

Calculation: to find the value of integral, first integrate and then simplify,

  $\begin{array}{l}{\displaystyle {\int }_0^1\frac{dx}{x^{0.5}}}={\left[\frac{x^{-0.5+1}}{-0.5+1}\right]}_0^1\text{ [}{\displaystyle \int x^n}=\frac{x^{n+1}}{n+1}]\\ {\displaystyle {\int }_0^1\frac{dx}{x^{0.5}}}={\left[\frac{x^{0.5}}{.05}\right]}_0^1\text{ [simplify]}\\ {\displaystyle {\int }_0^1\frac{dx}{x^{0.5}}}=2\sqrt{1}-2\sqrt{0}\\ {\displaystyle {\int }_0^1\frac{dx}{x^{0.5}}}=2-0\text{ [simplify]}\\ {\displaystyle {\int }_0^1\frac{dx}{x^{0.5}}}=2\end{array}$

Thus, the value of integral is $2$ .