= 0.5
You will need to use a calculator to solve for x. The answers are (to three decimal places): x =
−1.665 and x = +1.665.
We can find the area between the two curves by integrating the top curve minus the bottom
curve, using the points of intersection as the limits of integration. Because we want to find the
area in the first quadrant, we use 0 as the lower limit of integration. We get
We will need a calculator to evaluate this integral: dx ≈ 0.516.
- C The Trapezoid Rule enables us to approximate the area under a curve with a fair degree of
accuracy. The rule says that the area between the x-axis and the curve y = f (x), on the interval
[a, b], with n trapezoids, is
[y 0 + 2y 1 + 2y 2 + 2y 3 +...+ 2yn−1 + yn]
Using the rule here, with n = 4, a = 0, and b = 3, we get
- C Use your calculator to graph the second derivative and count the number of times that it crosses
the x-axis on the interval (−10, 10).
