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Solve the integral equation $f(x)=\pi\left(1+\int_{1}^{x} f(t) d t\right)$...

Question

Solve the integral equation $f(x)=\pi\left(1+\int_{1}^{x} f(t) d t\right)$

Solve the integral equation $f(x)=\pi\left(1+\int_{1}^{x} f(t) d t\right)$



Answers

If $ \displaystyle f(x) = \int^{\sin x}_0 \sqrt{1 + t^2} \, dt $ and $ \displaystyle g(y) = \int^y_3 f(x) \, dx $, find $ g''(\pi/6) $.


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