COMEDK · Maths · 30. Definite Integration
\(\int_\limits{-\dfrac{\pi}{2}}^{\dfrac{\pi}{2}} \sqrt{\cos x-\cos ^3 x} d x \text { is equal to }\)
- A 0
- B \(-\dfrac{2}{3}\)
- C \(-\dfrac{1}{3}\)
- D \(\dfrac{4}{3}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{4}{3}\)
Step-by-step Solution
Detailed explanation
The integral is \(I = \int_{-\pi/2}^{\pi/2} \sqrt{\cos x - \cos^3 x} dx\). Since \(\cos x - \cos^3 x = \cos x(1 - \cos^2 x) = \cos x \sin^2 x\), the integrand becomes \(\sqrt{\cos x \sin^2 x} = |\sin x| \sqrt{\cos x}\). The integral is…
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