Can someone help me? will rate Reverse the order of integration in the inte gral S...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates.∫R(x2+y)dA=∫∫drdθ.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.volume =∫∫∫dz dxdy.(b) polar coordinates.volume =∫∫drdθ. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
please anser 9,10,11 9. Reverse the order of integration in Jo edydr and then evae l integral. 10. Use polar coordinates to evaluate 12+y2 where R is the sector in the first quadrant bounded by y 0, y- z, and 11. Find the area of the surface on the cylinder y2 + z2-9 which is above the rectangle R-((,):0s 32, -3 S yS 3) 9. Reverse the order of integration in S e-dydz and then evaluate the integral 10. Use...
3] (a) Use Stoke's Theorem to evaluate ScF. dr by evaluating the related double inte- gral, where F(x, y, z) = (x2z, cy, 22) and C is the curve of intersection between the plane x+y+z=1 and the cylinder ? + y2 = 9 oriented clockwise when viewed from above. (b) Sketch a graph of both the plane and cylinder with so that the intersecting curve is clear. 2) Find the parametric equations for C and use them to sketch a...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
Sketch the region of integration, reverse the order of integration, and evaluate the integral. 27 3 03 dy dx y? + 1 3x Choose the correct sketch below that describes the region R from the double integral. O A. B. C. D. Ay y 3- 27- 3- 27 х х 27 27 3 What is an equivalent double integral with the order of integration reversed? X dx dy + 1
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. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. 2 1 2 X -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 2-y2 (2? + y) dA= (32 + y) dx dy + (x2 + y) dx dy. 2-y? (a) ketch the region of integration R in Figure 3. (b) By completing...
13. (5 points) Reverse the order of integration for the following iterated integral. You do not have to integrate. cos y dy dx 14. (5 points) Integrate the function g(r,0) = p sin over the sector of a disc in the first quadrant bounded by the circle r² + y2 = 1, the circle r² + y2 = 4, the line y = rV3, and the r-axis. 15. (5 points) Convert the following iterated integral from Cartesian to polar. You...
1. (6 marks) Find the volume of the solid enclosed by the paraboloid 2 = 1 - 22 - y2 and the coordinate planes of the first octant O = {(x, y, z) | x > 0, y > 0, z>0}. 2. (7 marks) Calculate SS/ (82 +93) dr dy dz. where E is the upper hemisphere x2 + y2 + 22 < 1 and 2 > 0. 3. (7 marks) Evaluate the integral SL (x + y) er?-y dA...
calculus 3. Answer all of the following, I will rate your work if you do so. Evaluate the double integral || xy2da, where Ris the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. Evaluate the iterated integral. 1 ya x-y xy dz dx dy xy dz dx dy 0 V The figure below shows the solid region Ein the first octant bounded by the...