Question

${\int }_0^{\pi /4}\frac{si{n}^{2}xco{s}^{2}xdx}{(si{n}^{3}x+co{s}^{3}x{)}^2}=$

• A. -1/6
• B. 1/6
• C. -1/3
• D. -1/2

Answer 1

The correct option is B

1/6

${\int }_0^{\frac{\pi }{4}}\frac{ta{n}^{2}xse{x}^{2}xdx}{(1+ta{n}^{3}x{)}^2}$

$ta{n}^{3}x=t$

$I=\frac{1}{6}$