Question

The value of \(\displaystyle \int_0^1 x(1-x)^5\,dx\) is:

• A. \(\frac{1}{12}\)
• B. \(\frac{1}{15}\)
• C. \(\frac{1}{18}\)
• D. \(\frac{1}{30}\)

Hint:

Recognize standard definite integrals to save time.

Answer 1

The Correct Option is B

Using Beta function property: \[ \int_0^1 x^m(1-x)^n dx=\frac{m!n!}{(m+n+1)!} \] Here \(m=1,\ n=5\): \[ =\frac{1!5!}{7!}=\frac{1}{15} \]