On page 226, do:

• Problem 1 *
  Do this problem by hand, and then use Maple (or Matlab, etc.) to check your result.

• Problem 2 *

• What is a functional?

• How does a functional differ from a function?

* NOTES:

1. In Problem 1, you are simply asked to evaluate the given integral by plugging in y(t) = – t.
   Notice that this is opposite the way such a problem would normally be addressed. Normally we would not be given a function y.
   Instead, we would be given the functional J and asked to determine what function y minimizes J.
   

2. In Problem 2, you are to plug the given function y(x) into the integral and evaluate the integral. The result will be a function of c₁ and c₂.
   Then use Calc-III to determine the values of c₁ and c₂ that minimize the result. You may use Maple (Matlab, etc.) as a tool to help you, but you might learn more if you do it by hand.

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