Use substitutions to evaluate indefinite integrals
Use the method of back substitution to solve tricker integrands
Use substitutions to evaluate definite integrals
Video6.1.1.U-substitution.
Finding antiderivatives "undoes" differentiation. So what happens when you undo Chain Rule, which was a rule about differentiation? You get u-substitution, and it will unlock way more integrands for us than we could do before.
Video6.1.2.U-substitution second example.
Let’s see another example.
Video6.1.3.Back Substitution.
Sometimes our integrands are a little trickier, and the u-substitution doesn’t clean up everything immediately. We can use back susbtitution to clean up the rest of the integrand. Typo: 5:52 should be (u-2)^2+4 as opposed to (u-2)^2-4. Challenge: Work out the rest of the problem based on that change!
Video6.1.4.U-substitution for Definite Integrals.
If you have a definite integral, you can still use u-substitution but you need to be careful about handling the limits of integration.
