Section

Content

Suggested Problems

Section 6.1

 Area between two curves y = f(x) and y = g(x), a ≤ x ≤ b,
 Process
 Subdivide the area into vertical strips
 Approximate area of vertical strip by rectangular area, R_{k}
 R_{k} ≈ [f(x_{k})  g(x_{k})]Δ(x_{k})
 Form Riemann sum of area approximations using rectangles
 Limiting case as Δ(x_{k}) → 0
 Integral solution:
 Subcases needed for area bounded between intersecting curves
 Area using horizonatal strips

Page 429: 13, 16, 18, 19, 25, 28, 30

Section 6.2

 Volume of solids with known crosssectional area
 Volume of solids of revolution (about xaxis or yaxis)
 Disk/Washer method
 Revolve area between two curves y = f(x) and y = g(x) about xaxis
 Integral solution:
 Shell Method
 Revolve area between two curves y = f(x) and y = g(x) about yaxis
 f(x) ≥ g(x) ≥ 0 on [a,b] where a ≥ 0
 Integral solution:
 Volumes of solids of revolution for areas bounded by two curves x = F(y) and x = G(y)
 Volumes of solids of revolution (about other horizontal or vertical lines)

Page 443: 1, 3, 13, 15, 21, 26, 30, 34, 35

Section 6.3

 Polar coordinate system
 Nonuniqueness of polar coordinates
 Converting polar coordinates to rectangular coordinates
 Converting rectangular coordinates to polar coordinates
 Graphs of equations given in polar coordinates
 Standard graphs
 Intersection points of graphs of equations given in polar coordinates
 Polar area
 Integral solution:

Page 456: 3, 4, 10, 12, 16, 23, 24, 31, 42, 44, 49

Section 6.4


Page 466: 5, 8, 15, 23, 25, 30, 38
