Subject: Calculus Research Questions
I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated.
Problem 1 can be done in two ways. First you could integrate and then differentiate twice.
The second method to solve this problem is to use the second form of the Fundamental Theorem of Calculus which says that
For your problem the upper limit in the integration is x3 so you need to use the chain rule when you differentiate. Hence
Now you can differentiate once more and evaluate at x = 1.
The average of g(x) on [1,3] is
Make the change of variables u = x + 1 then du = dx. When x = 0, u = 1 and when x = 1, u = 2. Thus
Hence k = 4.Cheers,