Q116 / 160 · TS EAMCET 2023 (12 May Shift 2) · Mathematics
$\int_0^{\frac{\pi}{2}} \sin ^6 \cdot x \cos ^4 \cdot x d x=$
- A$\frac{\pi}{256}$
- B$\frac{\pi}{512}$
- Correct answerC$\frac{3\pi}{512}$
- D$\frac{5\pi}{512}$
Solution
$$
I=\int_0^{\pi / 2} \sin ^6 x \cos ^4 x d x
$$
Using Walli's Formula,
$$
I=\frac{5 \times 3 \times 1 \times 3 \times 1}{10 \times 8 \times 6 \times 4 \times 2} \times \frac{\pi}{2}=\frac{3 \pi}{512}
$$
Hence, the correct answer is option: 'C'.