AP EAMCET · Maths · Definite Integration
\(\int_0^1 \sqrt{\frac{2+x}{2-x}} d x=\)
- A \(\pi+2\)
- B \(\frac{1}{2}(\pi+2)\)
- C \(\frac{\pi}{2}+2+\sqrt{3}\)
- D \(\frac{\pi}{3}+2-\sqrt{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{3}+2-\sqrt{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{I}=\int_0^1 \sqrt{\frac{2+x}{2-x}} d x ; \text { Let } u=\sqrt{\frac{2-x}{2+x}} \\ & \Rightarrow d u=\left(-\frac{1}{2 \sqrt{2-x} \sqrt{x+2}}-\frac{\sqrt{2-x}}{2(x+2)^{\frac{3}{2}}}\right) d x \\ & \Rightarrow d u=\left(-\frac{1}{2…
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