AP EAMCET · Maths · Definite Integration
\(\int_0^4 \frac{x+2}{\sqrt{4 x-x^2}} d x=\)
- A \(2 \pi\)
- B \(4 \pi\)
- C \(\pi\)
- D \(\pi / 2\)
Answer & Solution
Correct Answer
(B) \(4 \pi\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x+2}{\sqrt{4 x-x^2}} d x\) \(=\int \frac{(x-2)+4}{\sqrt{4-(x-2)^2}} d x\) \(\Rightarrow \quad \int \frac{(x-2)}{\sqrt{4-(x-2)^2}} d x+4 \int \frac{1}{\sqrt{4-(x-2)^2}} d x\) \(\Rightarrow \sqrt{4 x-x^2}+4 \sin ^{-1}\left(\frac{x-2}{2}\right)+c\)…
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