Question

$\underset{0}{\overset{1}{\int }}\frac{xdx}{(1-x{)}^{3/4}}=$

• A. $\frac{15}{16}$
• B. $\frac{3}{16}$
• C. $-\frac{3}{16}$
• D. $-\frac{16}{5}$

Answer 1

Answer: (D)

$\underset{0}{\overset{1}{\int }}\frac{xdx}{(1-x{)}^{3/4}}=-\underset{0}{\overset{1}{\int }}\frac{(1-x)-1}{(1-x{)}^{3/4}}dx$
$=-\underset{0}{\overset{1}{\int }}\left[(1-x{)}^{1/4}-(1-x{)}^{-3/4}\right]dx$
$={\left|\frac{(1-x{)}^{1/4}}{\frac{1}{4}}-\frac{(1-x{)}^{5/4}}{\frac{5}{4}}\right|}_0^1$
$=-4(0-1)+\frac{4}{5}(0-1)$
$=-\frac{16}{5}$