Find the integral that represents the volume of the following
solids:
1. below the surface z=1+xy and over the triangle with vertices
(1,1), (4,1) and (3,2).
2. enclosed by the planes y=0, z=0, y=x and 6x+2y+3z=6
The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is
intersected by the plane 2x - y = 1. The resulting intersection is
a curve on the surface. Find a set of parametric equations for the
line tangent to this curve at the point (1,1,-23/24).
Find the volume of the solid bounded by the surface z =5 +(x-4)
^2+2y and the planes x = 3, y = 3 and coordinate planes.
a. First find the volume by actual calculation.
b. Estimate the volume by dividing the region into nine equal
squares and evaluating the functional value at the mid-point of the
respective squares and multiplying with the area and summing it.
Find the error from step a.
c. Then estimate the volume by dividing each...
The finite region bounded by the planes z = x, x + z = 8, z =
y,
y = 8, and z = 0 sketch the region in R3 write the 6
order of integration. No need to evaluate. clear writing please