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Expert: - 2/28/2008


Question
How would you solve the following problem? Can it be done in the calculator?
Let R be the shaded region in the first quadrant enclosed by the graphs of y = e^-x^2, y = 1 - cos x, and the y-axis.
(a) Find the area of the region r.

Answer
If you have a calculator that can do integrals, it can be done.  Otherwise, find the intersection point of e^(-x^2) = 1-cos x, and the area is then the integral from 0 to the intersection point.

Given what has been said, the functions as I read them do not intersect at all in the first quadrant.

Taking e^(-x^2) - 1 + cos x = 0, there is no solution.
This can be seen since 1 - cos(x) > =0 and e^(-x^2) > 0.

Perhaps I am reading the functions wrong, so send me the correct functions please.  Thank you.

Calculus

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