are These the problem statements for the suggested problems for 5.8. In
general, you will get the problems from the textbook, but I will post questions
until everyone has a textbook.
6.1: 1,3,5,9,12,13,15,19,24,31
6.1 #1 Sketch a representative vertical or horizontal strip and nd the area
of the given regions bounded by the curves
y
y
= x2 + 6x 5
3
3
= x
2
2
6.1 #3 Sketch a representative vertical or horizontal strip and nd the area
of the given regions bounded by the curves
y
y
= sin 2x on [0, ]
=0
6.1 #5 Sketch a representative vertical or horizontal strip and nd the area
of the given regions bounded by the curves
x = y 2 5y
x =0
1
6.1 #9 Sketch the region bounded between the given curves and then nd
the area of the region.
y = x2 , y = x3
6.1 #12 Sketch the region bounded between the given curves and then nd
the area of the region.
y = 4x2 9, x = 3, x = 0, y = 0
6.1 #13 Sketch the region bounded between the given curves and then nd
the of area the region.
y = x4 3x2 , y = 6x2
6.1 #15 Sketch the region bounded between the given curves and then nd
the area of the region.
x = 2 y2 , x = y
6.1 #19 Sketch the region bounded between the given curves and then nd
the area of the region.
y = sin x, y = sin 2x, x = 0, x =
6.1 #24 Sketch the region bounded between the given curves and then nd
the area of the region.
y = ex , y =
1x 1
e + , x = 2, x = 2
2
2
6.1 #31 Imagine a cylindrical fuel tank of length L lying on its side; the
ends are circular with radius b. Determine the amount of fuel in the tank for a
given level by completing these steps:
a. Explain why the volume of the tank may be modeled by
b
b2 y 2 dy
V = 2L
b
2
b. Explain why the volume of fuel at level h (b h b) may be modeled
by
h
b2 y 2 dy
V (h) = 2L
b
c. Finally, for b = 4 and L = 20, numerically compute V (h) for h =
3, 2, . . . , 4. Note: V (0) and V (4) will serve as a check on your work.
3