double integrals over a region, triple integrals over a region, surface integrals, volume integrals

Upload: turtle

Post on 06-Jul-2018

216 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals

    1/5

  • 8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals

    2/5

  • 8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals

    3/5

    (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)'

    --------------------------------------------------------------------------------------------------------------------

  • 8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals

    4/5

    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

  • 8/18/2019 Double Integrals Over a Region, Triple Integrals Over a Region, Surface Integrals, Volume Integrals

    5/5

    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"