AP EAMCET · Maths · Definite Integration
\(\int_0^\pi\left(\sin ^5 x \cos ^3 x+\sin ^4 x \cos ^4 x+\sin ^3 x \cos ^4 x\right) d x=\)
- A \(\frac{873}{2240}\)
- B \(\frac{3 \pi}{128}+\frac{12}{35}\)
- C \(\frac{1641}{4480}\)
- D \(\frac{3 \pi}{128}+\frac{4}{35}\)
Answer & Solution
Correct Answer
(D) \(\frac{3 \pi}{128}+\frac{4}{35}\)
Step-by-step Solution
Detailed explanation
\(\int_0^\pi \sin^5 x \cos^3 x \, dx = 0\) \(\int_0^\pi \sin^4 x \cos^4 x \, dx = 2 \int_0^{\pi/2} \sin^4 x \cos^4 x \, dx = 2 \cdot \frac{3!! 3!!}{8!!} \frac{\pi}{2} = \frac{3 \cdot 1 \cdot 3 \cdot 1}{8 \cdot 6 \cdot 4 \cdot 2} \pi = \frac{3 \pi}{128}\)…
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