TS EAMCET · Maths · Definite Integration
\(\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos x}\) is equal to
- A \(\pi-2\)
- B \(\pi+2\)
- C \(\frac{\pi}{4}\)
- D \(2 \sin \frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(2 \sin \frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos x}\) ...(i) \(I=\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos \left(\frac{3 \pi}{4}+\frac{\pi}{4}-x\right)}=\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1-\cos x}\) ...(ii) From Eqs. (i) and (ii),…
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