Question

\( \int_{0}^{1} x(1 - x)^{99} \, dx = \)

• A. \( \frac{1}{10010} \)
• B. \( \frac{1}{1010} \)
• C. \( \frac{1}{10100} \)
• D. \( \frac{1}{10100} \)

Hint:

Beta function integrals of the form \( \int_0^1 x^m(1-x)^n dx \) directly reduce to factorial formNo need for lengthy integration.

Answer 1

The Correct Option is D