Question

What is ${\int }_0^{1}x{(1-x)}^{9}dx$ equal to?

• A. $\frac{1}{110}$
• B. $\frac{1}{132}$
• C. $\frac{1}{148}$
• D. $\frac{1}{240}$

Answer 1

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

We need to find ${\int }_0^{1}x(1-x{)}^{9}dx$

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

$={\int }_0^1(x^9-x^{10})dx$

$={[\frac{x^{10}}{10}-\frac{x^{11}}{11}]}_0^1$

$=\frac{1}{10}-\frac{1}{11}$

$=\frac{11-10}{110}$

$=\frac{1}{110}$

$\therefore {\int }_0^{1}x(1-x{)}^{9}dx=\frac{1}{110}$