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?
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.