Question

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

• A. 1/15
• B. 1/30
• C. -1/15
• D. 1/60

Answer 1

The correct option is B 1/30

${\int }_0^1(1-x{)}^{4}dx$
${\int }_0^{a}f\left(x\right)dx={\int }_0^{a}f(a-x)dx$
${\int }_0^{1}x(1-x{)}^{4}dx={\int }_0^1(1-x\left)\right(x^4)dx$
$={\int }_0^1(x^4-x^5)dx$
$={\int }_0^1{x}^4\cdot dx-{\int }_0^1{x}^{5}dx$
$=(\frac{x^5}{5}-\frac{x^6}{6}){\int }_0^1$
$=(\frac{1}{5}-\frac{1}{6})$
$=\frac{1}{30}$
${\int }_0^{1}x(1-x{)}^{4}dx=\frac{1}{30}$