JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int\limits_0^{\pi /2} {\frac{{{{\sin }^3}\,x}}{{\sin \,x\, + \,\cos \,x}}} \,dx\) is
- A \(\frac{{\pi \, - \,2}}{4}\)
- B \(\frac{{\pi \, - \,1}}{2}\)
- C \(\frac{{\pi \, - \,1}}{4}\)
- D \(\frac{{\pi \, - \,2}}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{{\pi \, - \,1}}{4}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{0}^{\pi / 2} \frac{\sin ^{3} x}{\sin x+\cos x} d x\) \(\Rightarrow \mathrm{I}=\int_{0}^{\pi / 4} \frac{\sin ^{3} x+\cos ^{3} x}{\sin x+\cos x} d x\) \(=\int_{0}^{\pi / 4}(1-\sin x \cos x) d x\) \(=\left(x-\frac{\sin ^{2} x}{2}\right)_{0}^{\pi / 4}\)…
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