double integrals over a region, triple integrals over a region, surface integrals, volume integrals
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8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals
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8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals
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(dB C dx dy dz)
'''where 0 is a scalar = a vector function, and B is a scalar'8onceptually, dB is an infinitesimal volume element'
he integral over a volume cannot be easily visualized, unli9eother types of integrals' (although the region being integratedA1=, can easily be graphed visualized)'
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8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals
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4 second, built on a progressive sac period of the *rst' but athird " based on the desire to return to the so-called olity ofthe second hat is too much' hree lts is too much' ''and arecipe for insty hat is too much'
• >ind the limits by algebraic elimination (if the e.uation interms of z (the third variable) I# provided) or graphing (ifno e.uation of any 9ind is provided)- the *rst set of limits
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will be in terms of the other two variables, the second setwill be in terms of the remaining variable, and the lastwill be (will 2181##4=I3? @1) a set of constants
• Integrate"