TS EAMCET · Maths · Indefinite Integration
If \(\frac{3 \pi}{2} < x < \frac{5 \pi}{2}\) and \(\int(\sqrt{1-\sin x}+\sqrt{1+\sin x})\) \(\mathrm{dx}=\mathrm{f}(\mathrm{x})+\mathrm{c}\) where \(\mathrm{c}\) is the constant of integration, then \(\mathrm{f}\left(\frac{\pi}{3}\right)-\mathrm{f}(0)=\)
- A 2
- B -2
- C \(2 \sqrt{2}\)
- D \(-2 \sqrt{2}\)
Answer & Solution
Correct Answer
(B) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x \\ & \because \frac{3 \pi}{2} \cos \frac{x}{2} \\ = & \int\left(\sqrt{\left(\cos \frac{x}{2}-\sin \frac{x}{2}\right)^2}+\sqrt{\left(\cos \frac{x}{2}+\sin \frac{x}{2}\right)^2}\right) d x \\ = &…
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