Download Calculus AP Name Volumes Day 2 Let R and S be the regions in the

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attached a second paper.
Calculus AP
Volumes Day 2
HW 5.8
This is the
HW for
Name ___________________________
the next
two nights
Let R and S be the regions in the first quadrant shown in the figure. The region R is bounded by
the x-axis and the graphs of y = 2 – x3 and y = tanx. The region S is bounded by the y-axis and the
graphs of y = 2 – x3 and y = tanx.
1. Find the area of R.
2. Find the volume of the solid generated when S is
revolved about the x-axis.
Let R be the region in the first quadrant bounded by the graph of y  2 x , the horizontal line
y  6 , and the y-axis, as shown in the figure below.
3. Find the area of region R. (No Calculator)
4. If the region R is revolved about the x-axis, determine the resulting volume. (Use your
calculator only for arithmetic if needed)
5. If the region R is revolved about the line y = -1, determine the resulting volume. (Use your
calculator only for arithmetic)
2
6. Let R be the region bounded by the graph of y  e 2x x and the
horizontal line y = 2. Determine the volume of the solid generated
when R is revolved about the line y = 1.
The shaded region, R, is bounded by the graph of y = x2 and the line y = 4 as shown in the figure.
7. Find the area of R.
8. Find the volume of the solid generated by revolving R about the x-axis.
b. There exists a number k, k > 4, such that when R is revolved about the line y = k, the resulting
solid has the same volume as the solid in part (b). Write, but do not solve, an equation involving an
integral expression that can be used to find the value of k.
Let f and g be the functions given by f(x) = 2x(1 – x) and g(x)  3(x  1) x for 0 < x < 1. The graphs
of f and g are shown in the picture below.
9. Find the volume of the solid generated when the shaded region is
revolved about the line y = 2.
10. Find the volume of the solid generated when the shaded region is
revolved about the line y = -3.
Let R be the region is the first quadrant enclosed by the graphs of y = 2x and
y = x2, as shown in the figure.
11. Find the area of this region. (No calculators)
12. If this region is revolved about the line y = -1, determine the resulting
volume. (No calculators)
13. Find the volume of the region R is revolved about the line y = 4. (You can use your calculators
if you want – but you wouldn’t have to!)