AP EAMCET · Maths · Definite Integration
\(\int_{-2 \pi}^{2 \pi} \sin ^4(2 x) \cos ^6(2 x) d x=\)
- A \(\frac{3 \pi}{64}\)
- B \(\frac{9 \pi}{64}\)
- C \(\frac{9 \pi}{35}\)
- D \(\frac{9 \pi}{280}\)
Answer & Solution
Correct Answer
(A) \(\frac{3 \pi}{64}\)
Step-by-step Solution
Detailed explanation
\(\int_{-2 \pi}^{2 \pi} \sin ^4(2 x) \cos ^6(2 x) d x = 2 \int_{0}^{2 \pi} \sin ^4(2 x) \cos ^6(2 x) d x\) Let \(u=2x \Rightarrow du=2dx\) \(= 2 \int_{0}^{4 \pi} \sin ^4(u) \cos ^6(u) \frac{1}{2} du = \int_{0}^{4 \pi} \sin ^4(u) \cos ^6(u) d u\)…
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