1. Consider the integral equation f(x)=1+2∫x3​f(t)dt where f(x) is an unknown function to be solved for. Equations of th

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1 Consider The Integral Equation F X 1 2 X3 F T Dt Where F X Is An Unknown Function To Be Solved For Equations Of Th 1 (88.02 KiB) Viewed 36 times

1. Consider the integral equation f(x)=1+2∫x3​f(t)dt where f(x) is an unknown function to be solved for. Equations of this type have applications to demographics. (a) Explain why any continuous function f that solves (1) must be differentiable. (b) Differentiate both sides of equation (1) to obtain a formula for f′(x) in terms of f(x). (c) Solve equation (1).