Question

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

• A. π/4
• B. π/2
• C. π/8
• D. π

Answer 1

The correct option is B

π/2

$LetI=2{\int }_0^{\frac{\pi }{2}}\frac{co{s}^{4}x}{co{s}^{4}x+si{n}^{4}x}dxLet{I}_1={\int }_0^{\frac{\pi }{2}}\frac{co{s}^{4}x}{co{s}^{4}x+si{n}^{4}x}dx\Rightarrow 2I_1=\frac{\pi }{2}=\frac{\pi }{2}\Rightarrow I_1=\frac{\pi }{4}\therefore I=\frac{\pi }{2}$