Question

${\int }_0^{\frac{\pi }{2}}\frac{si{n}^{4}x}{si{n}^{4}x+co{s}^{4}x}dx=$

• A. π/2
• B. π/3
• C. π/4
• D. 0

Answer 1

The correct option is C

π/4

$I={\int }_0^{\frac{\pi }{2}}\frac{si{n}^{4}x}{si{n}^{4}x+co{s}^{4}x}dx={\int }_0^{\frac{\pi }{2}}\frac{si{n}^{4}x}{si{n}^{4}x+co{s}^{4}x}dx$

$\Rightarrow 2I={\int }_0^{\frac{\pi }{2}}1dx\Rightarrow I=\frac{\pi }{4}$