5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, æ) æ(to) = x0, if and only if u is a solution to the integral equation x(t) = xo+ | f(s, x(8)) ds.
5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, æ) æ(to) = x0, if and only if u is a solution to the integral equation x(t) = xo+ | f(s, x(8)) ds.
5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, æ) æ(to) = x0, if and only if u is a solution to the integral equation x(t) = xo+ | f(s, x(8)) ds.
I can get from the differential equation to the integral equation using the FTOC, but I'm not sure how to incorporate u=u(t) for the actual problem
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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