Math CentralQuandaries & Queries


Question from Wanda, a parent:
Integral or Area of cos^2 X between pi/2 and 0.
The answer that I got is -pi/4. Is this correct? If not, how did you come up with your answer?


(1) The minus sign:

The function is nonnegative everywhere, but the integral from b to a of a function is the negative of the integral from a to b. This follows from the definition; and it is, as Martha Stewart would say, a good thing, because it means the formulas for piecing integrals together will still work when one of them is backwards.

(2) The value:

Get your son or daughter to draw the graph of cos2(x) from 0 to pi/2 carefully and cut out two copies. (Oh, OK, you may help.) Do they fit together into a rectangle? How big is it? What does this tell you about the area? Does this make sense in terms of what he or she found through calculus?

Good hunting!


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