Question

The value of ${\int }_0^{1}x(1-x{)}^{4}dx$ is

• A. $\frac{1}{12}$
• B. $\frac{1}{30}$
• C. $\frac{1}{24}$
• D. $\frac{1}{20}$

Answer 1

The correct option is B $\frac{1}{30}$

$I={\int }_0^{1}x(1-x{)}^{4}dx$

Applying property of definite integral $I={\int }_0^{a}f\left(x\right).dx={\int }_0^{a}f(a-x)dx$

$={\int }_0^1(1-x)x^{4}dx$

$={\int }_0^1{x}^4-x^{5}dx$

$={[\frac{x^5}{5}-\frac{x^6}{6}]}_0^1$

$=\frac{1}{5}-\frac{1}{6}$

$=\frac{1}{30}$.