Question

What is the value of $\stackrel{1}{\underset{0}{\int }}x(1-x{)}^{9}dx?$

• A. $\frac{1}{10}$
• B. $\frac{1}{11}$
• C. $\frac{1}{90}$
• D. $\frac{1}{110}$
  

Answer 1

The correct option is D $\frac{1}{110}$

Apply integration by parts.

I $={\int }_0^{1}x{(1-x)}^{9}dx$

$={|-\frac{x{(1-x)}^{10}}{10}|}_0^1+{\int }_0^1\frac{{(1-x)}^{10}}{10}dx$

$=0+\frac{1}{110}$

$=\frac{1}{110}$