Homework SourseFind a function fx such that 9the integral a to xftt2 dt 4s
Find a function f(x) such that
9+(the integral a to x)f(t)/t^2 dt = 4sqrt(x)
9+(the integral a to x)f(t)/t^2 dt = 4sqrt(x)
Solution
(the integral a to x)f(t)/t^2 dt=4x-9
d ((the integral a to x)f(t)/t^2 dt)/dx =d(4x-9)/dx
f(x)/x2=2/x
f(x)=x2*2/x=2xx
I used the fact that d(axg(t)dt)/dx=g(x) which is the fundamental theorem of calculus
