AP EAMCET · Maths · Definite Integration
\(\int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x d x\) is equal to
- A \(\frac{3 \pi}{128}\)
- B \(\frac{3 \pi}{256}\)
- C \(\frac{3 \pi}{572}\)
- D \(\frac{3 \pi}{64}\)
Answer & Solution
Correct Answer
(B) \(\frac{3 \pi}{256}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x d x=2 \int_0^{\pi / 2} \sin ^4 x \cos ^6 x d x \\ &=\frac{2 \frac{4+1}{2} ! \frac{6+1}{2} !}{2 \frac{4+6+2}{2} !} \\ &=\frac{\frac{3}{2} \cdot \frac{1}{2} \sqrt{\pi} \cdot \frac{5}{2} \cdot \frac{3}{2} \cdot…
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