Find the Average of f(x) On a Given Interval From This Integral Equation
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Find the Average of f(x) On a Given Interval From This Integral Equation
If a continuous function f(x) satisfies π/2 ∫ f(t−x)f(t)dt=cos^4(x), x find the average value of f(x) on [0,π/2]. Key ideas: Integrate both sides with respect to x. Rewrite the left side as a double integral. Use the substitutions u=t−x and v=u+x to convert the region into the triangle: u[0: v], v[0:L], where L=π/2. By symmetry, that ...
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