ANSWERS AND EXPLANATIONS TO SECTION II
1.
Let R be the region in the first quadrant shown in the figure above.
(a) Find the area of R.
In order to find the area, we “slice” the region vertically and add up all of the slices. We use
the formula for the area of the region between y = f (x) and y = g(x), from x = a to x = b,
[f(x)−g(x)] dx
We have
f (x) = 4 − x^2 and g(x) = ex
Next, we need to find the point of intersection in the first quadrant. Use your calculator to find
that the point of intersection is x = 1.058 (rounded to three decimal places). Plugging into the
formula, we get
[4−x^2 −ex] dx
Evaluating the integral, we get = = 1.957.
