Integration by substitution

Try integrating: Hint: Try a guess and differentiate it. Answer: That was easy to guess, but lets try it with substitution: Let So we have: (the dx is a problem) So, That’s a simple one …. now let’s try a harder one ……..

Try this integral: so, and Re-write your integral: Integrate and then substitute:

Now try some of your own (about 10 minutes). 1. 2. 3. 4. 5.

What about definite integration? Take the upper and lower values of x from the integral and find the corresponding values of u. Now re-write the integral in terms of u, as you did before. Confirm this result by using your Graphics Calculator.

Now some of your own (about 10 minutes). 1. 2. 3.

One step beyond…. Try this one:- (too easy!) Something wrong? - That x, but …….