Correct Answer - Option 3 : 2
Concept:
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Definite Integral: If ∫ f(x)dx = g(x) + C, then \(\rm \displaystyle \int_a^b f(x)\ dx = [ g(x)]_a^b=g(b)-g(a)\).
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\(\rm \displaystyle \int x^n\ dx=\dfrac{x^{n+1}}{n+1}\).
Calculation:
\(\rm \displaystyle \int \dfrac{1}{\sqrt x }\ dx= \int x^{-\tfrac{1}{2}}\ dx\).
\(\rm=\dfrac{x^{-\tfrac{1}{2}+1}}{-\tfrac{1}{2}+1}+C\)
\(\rm =2\sqrt x+C\)
\(\rm \displaystyle \therefore \int_4^9 \dfrac{1}{{\sqrt x }}\ dx = [2\sqrt x]_4^9=2[\sqrt 9 - \sqrt 4]=2(3-2)=2\).
