Worksheet 7.2 and 7.3 Intro
Name: ____________________________________
For each question, set up the integral, then evaluate on your calculator.
1. Find the area of the shaded region.
2. Find the area of the shaded region.
3. Find the area of the region enclosed by
.
Use dy’s:
OR
Use dx’s:
4. Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and on the
right by the curves y = sin x and y = cos x.
5. Is the following statement always, sometimes, or never true?
The area of the region between the graphs of the continuous functions y = f(x) and y = g(x) and the
vertical lines x = a and x = b with a < b is:
6. Let f and g be the functions given by f(x) = ex and g(x) = 1/x. Which of the following gives the area of the
region enclosed by the graphs of f and g between x = 1 and x = 2?
7. Let R be the region in the first quadrant bounded by the x-axis, the graph of x = y2 + 2 and the line x = 4.
Which of the following integrals gives the area of R?
8. Find the volume of the solid whose base is the region contained between the parabolas y = x 2 and y = 2 – x2
and whose cross-sections are circular disks with diameters that run from y = x2 to y = 2 – x2.
V=