Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
$\int_0^{\frac{\pi}{2}} \sin ^6 \cdot x \cos ^4 \cdot x d x=$
MathematicsDefinite IntegrationTS EAMCETTS EAMCET 2023 (12 May Shift 2)
Options:
  • A $\frac{\pi}{256}$
  • B $\frac{\pi}{512}$
  • C $\frac{3\pi}{512}$
  • D $\frac{5\pi}{512}$
Solution:
2189 Upvotes Verified Answer
The correct answer is: $\frac{3\pi}{512}$
$$
I=\int_0^{\pi / 2} \sin ^6 x \cos ^4 x d x
$$
Using Walli's Formula,
$$
I=\frac{5 \times 3 \times 1 \times 3 \times 1}{10 \times 8 \times 6 \times 4 \times 2} \times \frac{\pi}{2}=\frac{3 \pi}{512}
$$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.