The value of 8/(π) int_0^(π)/2 dfrac(cos x)^2023(sin x)^2023 + (cos x)^2023 dx is __________

The value of 8/(π) int_0^(π)/2 dfrac(cos x)^2023(sin… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.) · numerical answer

The value of

\dfrac{8}{\pi} \int_{0}^{\frac{\pi}{2}} \dfrac{(\cos x)^{2023}}{(\sin x)^{2023} + (\cos x)^{2023}}\, dx

is __________

Show answer and solution

Answer: 2

Solution

Using the property that ∫₀^(π/2) f(cos x)/(f(sin x) + f(cos x)) dx = π/4, the integral equals π/4.

Therefore (8/π) · (π/4) = 2.

[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]

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