Section 2.9 I. Set up a double integral to compute the volume of the solid under...
4 Set up and evaluate a double integral to find the volume of the solid bounded by the graph of the equations y # 4-x2.z # 4-r2, first octant
Do both questions and show all steps for good rating. Thanks. 7. Set up an iterated double integral to compute the volume of the solid bounded above by r2 y and below by the region R that is a triangle in the ry-plane with vertices (0,0), (0,3) and (5,3). z = (8) Do not evaluate. Exam 2-u ath 260-01 8. Set up a double integral in polar coordinates to find the volume of the solid bounded by zry 2 =...
7. Set up and evaluate an integral that represents the volume of the solid under the plane y-z = 1 and above the bounded region enclosed by x 2y-y2 and x + y -4 For full credit, you must draw the region, find the points of intersection and show all steps. 7. Set up and evaluate an integral that represents the volume of the solid under the plane y-z = 1 and above the bounded region enclosed by x 2y-y2...
30 points) (a) (12 points) Set up an integral representing the volume of the solid obtained by rotating about the x-axis the region bounded by y = x3 + 1, x = 0, x = 2, and y= 1. You do not need to evaluate the integral. (b) (18 points) Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x – x2 and y= 0.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane. 4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid in the first octant bounded by the coordinate planes and the plane z = 5 - x - y
6. Set up, but do not evaluate, an iterated integral that gives the volume of the solid region that lies below the paraboloid z =エ2 + V2 and above the region in the zy-plane bounded by the curves-8a2 and i-z. 6. Set up, but do not evaluate, an iterated integral that gives the volume of the solid region that lies below the paraboloid z =エ2 + V2 and above the region in the zy-plane bounded by the curves-8a2 and i-z.
Question 8 8 pts (8) Set up a double integral that represents the volume of the solid under the surface z- 3+ y2 = 1 and above the region in the zy-plane enclosed by y = |e) and y = 4.
Set up, but DO NOT evaluate an integral to find the volume of the following solid: The solid generated by rotating the region bounded between y=1+sec x, y = 3, 2 = 7/3, and x = -7/3 about the line y = 1. Use the washer method.
Consider the following. ebr (a) Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radi br and aR. (Let a-8 and b-5) dy (b) By interpreting the integral as an area, find the volume V of the torus.