TS EAMCET · Maths · Definite Integration
\(\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x=\)
- A \(\frac{1}{2}\)
- B \(\frac{3}{2}\)
- C 2
- D 1
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(I=\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x\) ...(i) \(\because \int_a^b f(x) d x=\int_a^b f(a+b-x) d x\) \(I=\int_3^6 \frac{\sqrt{9-x}}{\sqrt{x}+\sqrt{9-x}} d x\) ...(ii) Add (i) and (ii),…
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