Do both questions and show all steps for good rating. Thanks. 7. Set up an iterated...
5. Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order. ∫∫Dy dA, D is bounded by y = x - 20; x = y2 9. Find the volume of the given solid. Bounded by the planes z = x, y = x,x + y = 7 and z = 0 14. Evaluate the double integral. ∫∫D 4y2 da, D = {(x,y) I-1 ≤ y ≤ 1, -y - 2 ≤ 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.
please write neatly and no script! 8. (10 points) (a) Using rectangular coordinates, set up an iterated integral that represents the volume of the solid bounded by the surfaces z = x2 + y2 +3, z = 0, and x2 + y2 = 1. (b) Evaluate the iterated integral in (a) by converting to polar coordinates.
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.
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
2 integral giving the surface area of the portion of (3) Set up, but do not evaluate, an 2m2+e above the triangle with vertices (0,0), (0,5) and (3,5). (4) Change the following points from rectangular coordinates into the specified coordi- nate systemn: (a) (-3,-3,9), Cylindrical Coordinates. (b) (V3,1,0), Spherical Coordinates. 2 integral giving the surface area of the portion of (3) Set up, but do not evaluate, an 2m2+e above the triangle with vertices (0,0), (0,5) and (3,5). (4) Change...
1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3. Use Groen's Theorem to set up an iterated double integral equal to the line integral $+eva) dx +(2+ + cow y) dy where is the boundary of the region enclosed by the parabolas y rand 1 = y2 with positive orientation. This yields: A. where R is the triangular region with vertices (0,0),(1,0) and (0,1) is: A B. B. So ['(2-z) dr de SL...
7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte-gral which represents the volume of the ice cream cone bounded by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian coordinates. 7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte- gral which represents the volume of the ice cream cone bounded by the cone z = Vr2 + y2 and the hemisphere z = 18 - 22 - y2 using...
Please show full solutions so i can understand 3. (i) 3pl Set up iterated integrals for both orders of integration forev dA, where D is the region in the ry-plane bounded by y -,4, and z-0 (ii) [3p] Evaluate the double integral in part (i) of this question using the easier order of integration. (ii) [3pl Find the average of the function f(, y) yey over the region D. 3. (i) 3pl Set up iterated integrals for both orders of...
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