Mathematics · Integral Equations

Let f(x) = x + a π 2 - 4 sin x + b π 2 - 4 cos x, x &in; R be a function which satisfies the integral equation f(x) = x + ∫ 0 π/2 sin(x + y) f(y) dy. Then the value of (a + b) is equal to:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

-2π(π + 2)

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Let f(x) = x + a &pi; 2 - 4 sin x + b &pi; 2 - 4 cos x, x &in; R be a function which satisfies the integral equation f(x) = x + &int; 0 &pi;/2 sin(x + y) f(y) dy. Then the value of (a + b) is equal to: