Substitution Method for Definite Integrals **careful!**

Description: For definite integrals - those with limits of integration - the method of substitution works more or less exactly as for indefinite integrals. However, we have to be careful to change the limits of integration as well!

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

[naiko]

I'd like to point out that inside definite integrals du and dx are very different!
In fact if one remembers riemann sums dx = (B-A)/n, with n->infinity
But since in the new integral with u we had to change the A and B into g(A) and g(B), then dx and and du = (g(B) - g(A))/n are different !!
And since f'(u) and f'(g(x)) are equal after changing the limits of integration it musts mean that the remaining parts inside the integrals must be equivalent as well.
In other words g'(x)*dx = u' *du, bust since u is a variable u' = 1 and therefore g'(x)*dx = du

[qqtrol]

I think it's just easier to compute indefinite integral in terms of x and think about a specific definite one.

[yesserlabidi]

I'm going to multiply the top and multiply the bottom by 3.

what did u mean by this pls ????

[makisekurisu]

A bit confusing as some of the words you said wasn't a visual, but I think it's a decent vid

[spacepanda]

Sorry, didn't get the part where we multiply the integral by 1/3 to get 3dx. Why are we left with 1/3 but not 3 before integral? Thank you for answer