AP EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \frac{\sin ^3 x \cos x d x}{\sin ^4 x+\cos ^4 x}=\)
- A \(\pi\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{8}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
\(=\int_0^{\pi / 2} \frac{\sin ^3\left(\frac{\pi}{2}-x\right) \cos \left(\frac{\pi}{2}-x\right)}{\sin ^4\left(\frac{\pi}{2}-x\right)+\cos ^4\left(\frac{\pi}{2}-x\right)} d x\) Adding Eqs. (i) and (ii), we get…
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