Question

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

Answer 1

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

Answer 2

\[\int_{0}^{1}\int_{x^4}^{x}\int_{0}^{ x+2y-z}\ dz.dy.dx\]

Answer 3

i spose z = x+2y; so we can change that

Answer 4

\[\int_{0}^{1}\int_{x^4}^{x}\int_{0}^{ x+2y}\ dz.dy.dx\]
\[\int_{0}^{1}\int_{x^4}^{x}x+2y\ dy.dx\]
\[\int_{0}^{1}(xx+x^2)-(xx^4+(x^4)^2)\ dx\]
\[\int_{0}^{1}2x^2-x^5-x^8\ dx\]
\[\frac23-\frac16-\frac19\]

Answer 5

once your comfortable in your directions from here to there; you just work it from the inside out