TS EAMCET · Maths · Definite Integration
\(\int_{-4}^5 \frac{1}{\sqrt{20+x-x^2}} d x=\)
- A \(\frac{81 \pi}{8}\)
- B \(\frac{9 \pi}{2}\)
- C \(\pi\)
- D \(\frac{\pi}{10}\)
Answer & Solution
Correct Answer
(C) \(\pi\)
Step-by-step Solution
Detailed explanation
\(\int_{-4}^5 \frac{1}{\sqrt{20+x-x^2}} d x = \int_{-4}^5 \frac{1}{\sqrt{\frac{81}{4} - \left(x-\frac{1}{2}\right)^2}} d x\) \(= \left[\arcsin\left(\frac{x-\frac{1}{2}}{\frac{9}{2}}\right)\right]_{-4}^5\) \(= \left[\arcsin\left(\frac{2x-1}{9}\right)\right]_{-4}^5\)…
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