2) The basic side of a prism is the triangle in the xy-plane, which is limited by the x-axis and the
lines y=x and x=1. The
upper limit of the prism is the plane z= f(x,y)=4-x-y. Calculate the volume of the prism.
Note: First draw the triangle and integrate f over the triangle.
3) Calculate the integral
D R R2
is the area in the plane
which is limited by the parabola y = x2 and the line y= 6-x.
Note: First draw D and determine the point of intersection between the line and the parabola
to calculate the integral.
A geometric solid is below the surface Z = 15 x2 y2 and above the area D, whichis limited by
the x-axis, the line
5) y = 4x-2 and the curve y = 2vx. Calculate the volume of the solid.
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