anonymous
  • anonymous
Find the volume of the given solid: Under the plane x+2y-z= 0 and above the region bounded by y = x and y = x^4 Please explain step by step
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
well; z is from 0 to x+2y-z and x looks to be from the roots of y = x^4 and y is from 0 to x maybe; but it helps if you draw the Region to determine how your x and y moves
amistre64
  • amistre64
|dw:1333481851611:dw|
amistre64
  • amistre64
\[\int_{0}^{1}\int_{x^4}^{x}\int_{0}^{ x+2y-z}\ dz.dy.dx\]

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amistre64
  • amistre64
i spose z = x+2y; so we can change that
amistre64
  • amistre64
\[\int_{0}^{1}\int_{x^4}^{x}\int_{0}^{ x+2y}\ dz.dy.dx\] \[\int_{0}^{1}\int_{x^4}^{x}x+2y\ dy.dx\] \[\int_{0}^{1}(xx+x^2)-(xx^4+(x^4)^2)\ dx\] \[\int_{0}^{1}2x^2-x^5-x^8\ dx\] \[\frac23-\frac16-\frac19\]
amistre64
  • amistre64
once your comfortable in your directions from here to there; you just work it from the inside out
anonymous
  • anonymous
Thank you so much! I understood it.
amistre64
  • amistre64
youre welcome, and with any luck its even correct :)

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