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Find the volume of the given solid: Under the plane x ? 2y + z = 3 and above the

ID: 3288029 • Letter: F

Question

Find the volume of the given solid: Under the plane x ? 2y + z = 3 and above the region bounded by x + y = 1 and x^2 + y = 1

Explanation / Answer

Points of intersection:------ x^2 + y = x + y ==> x = 0, 1.------- Note that for x in (0, 1), we have 1 - x^2 > 1 - x.----------- So, the volume equals--------- ?(x = 0 to 1) ?(y = 1 - x to 1 - x^2) (3 - x + 2y) dy dx------ = ?(x = 0 to 1) [(3 - x)y + y^2] {for y = 1 - x to 1 - x^2} dx--------- = ?(x = 0 to 1) [(3 - x)(x - x^2) + (1 - x^2)^2 - (1 - x)^2] dx---------- = ?(x = 0 to 1) (x^4 + x^3 - 10x^2 + 8x) dx---------- ---------------ask me if you need any help

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