Section
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Content
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Suggested Problems
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Section 6.1
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- 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, Rk
- Rk ≈ [f(xk) - g(xk)]Δ(xk)
- Form Riemann sum of area approximations using rectangles
- Limiting case as |Δ(xk)| → 0
- Integral solution:
- Subcases needed for area bounded between intersecting curves
- Area using horizonatal strips
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Page 429: 13, 16, 18, 19, 25, 28, 30
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Section 6.2
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- Volume of solids with known cross-sectional area
- Volume of solids of revolution (about x-axis or y-axis)
- Disk/Washer method
- Revolve area between two curves y = f(x) and y = g(x) about x-axis
- Integral solution:
- Shell Method
- Revolve area between two curves y = f(x) and y = g(x) about y-axis
- 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)
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Page 443: 1, 3, 13, 15, 21, 26, 30, 34, 35
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Section 6.3
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- Polar coordinate system
- Non-uniqueness 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:
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Page 456: 3, 4, 10, 12, 16, 23, 24, 31, 42, 44, 49
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Section 6.4
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Page 466: 5, 8, 15, 23, 25, 30, 38
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