Question

\(\int_1^9 \frac{dx}{\sqrt{x}} \)

• A. 8
• B. 4
• C. 2
• D. 12

Hint:

For integrals involving \( x^{-\frac{1}{2}} \), use the power rule for integration and simplify the result.

Answer 1

The Correct Option is A

We are given: \[ I = \int_1^9 \frac{dx}{\sqrt{x}} \] This can be written as: \[ I = \int_1^9 x^{-\frac{1}{2}} \, dx \] Using the power rule: \[ I = \left[ 2x^{\frac{1}{2}} \right]_1^9 = 2(9^{\frac{1}{2}}) - 2(1^{\frac{1}{2}}) = 2(3) - 2(1) = 6 - 2 = 8 \] Thus, the correct answer is \( 8 \).