multiple integral iteration solutions (and examples)

2d quarter moon exercise:

• int2dexercise.pdf
• int2dexercise-soln.pdf
• int2dexercise.mw
  

triple integral exercise:

• tripleintx.htm
• tripleintx-soln.htm [includes PDF and MW links]

homework (some example)  problem solutions:

• double integrals:
  [See this worksheet to help with polar coord iteration diagrams, this one for cartesian examples too.]
• s15-3-e4.mw volume under surface over a circle (inside a cylinder)
• s15-3-poolexample.mw volume of a cardioid bounded pond
• s15-3-3.mw changing to polar coordinates in a double integral over a triangle
• s15-3-17.mw area between two polar curves
• s15-3-35.mw circular pool with linear depth in one direction: volume
• s15-3-36.mw volume of revolution evaluated in polar coordinates
• s15-4-5.mw 2d centroids, centers of mass, triangles etc
• s15-4-normal2d.mw probability
• s15-4-probability.mw
• triple integrals:
• handout: example of setting up, iterating triple integral 6 different ways,
  2-d outer double integral diagrams [tripleintexample.mw];
  
• 15.6.ex3 [pdf] changing iteration to adapt to rotational symmetry; parabola of revolution solid
• s15-6-13.mw [short answers for 21, 27]
• s15-6-21.mw [bonus: centroid and center of mass]
• s15-6-23.mw [setup triple integral, centroid]
• s15-6-31.mw [ s15-6-31-volume.mw, tripleint-s15-6-31.pdf]
• s15-6-33.mw  [deconstruct triple integral, 2-d outer double integral diagrams]
• s15-6-34.mw  [deconstruct triple integral, 2-d outer double integral diagrams]
• s15-6-35.mw  [deconstruct triple integral, centroid]
• center of mass, centroid:
• s15-6-40.mw
• s15-6-41.mw
• s15-6-42.mw
• s15-7-20.mw

line integrals etc:

• s16-1-19.mw  2d and 3d fieldplots and field lines
• s16-1-33.mw  linear approximation to vector field flow lines
• s16-2-27.mw  line integral of vector field
• s16-2-31.mw line integral of a scalar
• s16-2-36.mw center of mass of a homogeneous semicircular wire and an inhomogeneous helical wire (line integral of scalar)
• s16-2-45.mw line integral on a helix (and conservative vector field: gravity)
• s16-2-48.mw line integral of a scalar (area of circular fence)
   [s16-2-48-soln.mw]
• s16-3-35.mw counter-example to existence of a "global potential" function: theta(x,y)
• s16-3-x1.mw inverse square force (conservative!)
• s16-4.mw line integral version of Green's theorem
• s16-4-18.mw use Green's thm to calculate line integral
• s16-4-19.mw area of one loop of a cycloid with Green's theorem
• s16-5-9-11.htm [s16-5-9-11soln.htm] curl and divergence in the plane from the rates of changes of the components
• s16-6-33.mw a tilted parabolic cylinder surface example: surface integrals
• s16-7-23.mw a parabolic of revolution graph surface example: surface integrals