Login

Welcome, Guest. Please login or register.

March 29, 2024, 11:41:19 pm

Author Topic: Fundamental Theorem of Calculus  (Read 689 times)  Share 

0 Members and 1 Guest are viewing this topic.

#1procrastinator

  • Guest
Fundamental Theorem of Calculus
« on: July 16, 2012, 01:26:25 pm »
0
IF you have a function f(t) and you integrate from a fixed number a to a variable x, can the independent variable also be the upper limit of integration?

Then when you differentiate it with respect to x, why do you get f(x) and not f(t)? If we were to integrate it again, would we then have to use a different variable for the upper limit?

fred42

  • Victorian
  • Forum Regular
  • **
  • Posts: 84
  • Respect: +12
Re: Fundamental Theorem of Calculus
« Reply #1 on: July 17, 2012, 10:24:14 pm »
0
When integrating w/r/t a variable, you can't then use the same variable to substitute (let x = x???). If we want the solution to the integral to be a function of x, we use a different variable, in this case t as the function to be integrated.