TS EAMCET · Maths · Definite Integration
\(\int_0^2 \sqrt{(x+3)(2-x)} d x=\)
- A \(\frac{25}{8} \operatorname{Cos}^{-1}\left(\frac{1}{5}\right)-\frac{\sqrt{6}}{4}\)
- B \(\frac{25}{8} \operatorname{Sin}^{-1}\left(\frac{1}{5}\right)-\frac{\sqrt{6}}{4}\)
- C \(\frac{\pi}{2}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(A) \(\frac{25}{8} \operatorname{Cos}^{-1}\left(\frac{1}{5}\right)-\frac{\sqrt{6}}{4}\)
Step-by-step Solution
Detailed explanation
\( \int_0^2 \sqrt{(x+3)(2-x)} d x = \int_0^2 \sqrt{-x^2-x+6} d x = \int_0^2 \sqrt{\frac{25}{4} - \left(x+\frac{1}{2}\right)^2} d x \)…
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