Fundemental theorem of Calc. question?

[Integral8850]

Homework Statement

Find function f(x) and constant a such that,

6+ integral f(t)/t^2 dt = 2x
limits are a to x

Homework Equations

I think I am on the right track could someone check this?

The Attempt at a Solution

if x = a then the integral will = 0,
6 = 2a, a = 3 limits now are 3 to x,
now,
6 + integral f(x)/x^2 dx = 2x, fundamental theorem
6 + f(x)/x^2 = 2 => 6 + f(x)= 2x^2 => f(x)= 2x^2 - 6
Thanks!

 

[sutupidmath]

try to take the derivative of both sides and see what happens?
on your last line, when you took the derivative, you missed something. what is the derivative of 6?

 

[Integral8850]

Ok thanks that was the part I was not sure about so the derivative of 6 goes to 0.
Thanks!