Question

What is the value of ${\int }_4^9\frac{1}{\sqrt{x}}dx$ ?

• (A) $1$
• (B) $-2$
• (C) $2$
• (D) $-1$

Answer 1

The Correct Option is C

Explanation:
$\int \frac{1}{\sqrt{x}}dx=\int x^{-\frac{1}{2}}dx$$=\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C$$=2\sqrt{x}+C$$\therefore {\int }_4^9\frac{1}{\sqrt{x}}dx=[2\sqrt{x}{]}_4^9=2[\sqrt{9}-\sqrt{4}]=2(3-2)=2$Hence, the correct option is (C).