Find the volume of the solid in R 3 .I need to find the volume of the solid in R 3 . It is bounded by the following: y = x 2 , x = y 2 , z = x + y + 21 and z = 0.I known that the volume is expressed as follows: ∭ 1 d VI have trouble finding the correct limits of integration for this problem.

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Find the volume of the solid in             R        3  .I need to find the volume of the solid in             R        3  . It is bounded by the following:   y  =      x    2  ,   x  =      y    2  ,   z  =  x  +  y  +  21 and   z  =  0.I known that the volume is expressed as follows:  ∭  1    d  VI have trouble finding the correct limits of integration for this problem.

Trevor Copeland · Accepted Answer

Step 1The projection of the solid on the xy plane is the region enclosed by the parabolas   y  =      x    2   and   x  =      y    2  . These intersect at (0,0) and (1,1) and form the shape of a leaf.Step 2Then:   0  ≤  x  ≤  1 and       x    2    ≤  y  ≤      x  .z  moves from 0 towards the plane   x  +  y  +  21  =  z.Therefore:   V  =      ∫    0    1        ∫                  x        2                            x                  ∫    0          x      +      y      +      21        d  z  d  y  d  x

Find the volume of the solid in mathbb{R}^3. It is bounded by the following: y=x^2, x=y^2, z=x+y+21 and z=0.

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