Consider the function defined by the rule where .

Compute and exactly.

Use the First Fundamental Theorem of Calculus to find an equivalent formula for that does not involve integrals. That is, use the first FTC to evaluate .

Observe that is a linear function; what kind of function is ?

Using the formula you found above for , that does not involve integrals, to compute .

While we have defined by the rule , it is equivalent to say that is given by the rule . What do you observe about the relationship between and ?

You can earn partial credit on this problem.