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(5) Double Integrals M = } } Vå sin(x) dxdy 0 y2 (5a) Find the region...
sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region....
sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region. (10pc
(y=2 • A region is bounded by 3 functions: {x = y2 as shown. Clearly x=y...
(y=2 • A region is bounded by 3 functions: {x = y2 as shown. Clearly x=y construct a double integral to find its area using both dydx and dxdy orders. You do not need to evaluate the integral. 2
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find ...
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the region R in the ry-plane bounded by the curve y --x? +2x and the line y - x-2, while the top of the solid is bounded by the surface z xy e"
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the...
13. Use double integrals to find the area inside the curve r = 1 +sin 14. (a) Express f Io ry dy ...
14 only
13. Use double integrals to find the area inside the curve r = 1 +sin 14. (a) Express f Io ry dy dr as an integral over the triangle D, which is the set of (u. v) where 0s u s 1, 0 ssu (HINT: Find a one-to-one mapping T of D onto the glven region of integration.) (b) Evaluate this integral directly and as an integral over D* 15. Integrate ze+ over the cylinder
13. Use double...
11.1) a) Verify that the function f(x,y) given below is a joint density function for r...
11.1) a) Verify that the function f(x,y) given below is a joint density function for r and y: ſ4.ty if 0 <r<1, 0 <y<1 f(x, y) = { 10 otherwise b) For the probability density function above, find the probability that r is greater than 1/2 and y is less than 1/3. 11.2) For the same probability density function f(x,y) as from Problem #1. Find the expected values of r and y. 11.3) a) Let R= [0,5] x [0,2]. For...
1. Find the mass and centroid of the region bounded by the = y2 with p...
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
1.1. Find the absolute and minimum values of f(x, y) = xy? on the set D=...
1.1. Find the absolute and minimum values of f(x, y) = xy? on the set D= {(x, y)\x² + y si 1.2. Find the extreme values of f(x,y) = x² + y2 + 4x-4y, using the Lagrange multipliers, with the constraint x² + y² 59 1.3. Evaluate the integral - Le*dxdy 1.4. Evaluate the integral L1.** sin(x+ + gydydx 1.5. Find the area of the surface x + y2 +22 - 4 that lies above the plane z = 1....
1. Let R be the region enclosed by the curves y =ra and r = y2 Nole that there is no med to evaluate any integrals in this problem unless you run out of other things to do). a) Find a dy integral for...
1. Let R be the region enclosed by the curves y =ra and r = y2 Nole that there is no med to evaluate any integrals in this problem unless you run out of other things to do). a) Find a dy integral for the volume of the solid obtained by rotating R about the r-axis. (Compare with your solution to part f of the last worksheet). b) Find a dx integral for the volume of the solid obtained by...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a) [2 points] First order b) [2 points] Second order c) [6 points] Evaluate the integral using the more convenient order
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
only final answer , no explaining required Question 13 Find the equation of the plane tangent...
only final answer , no explaining required
Question 13 Find the equation of the plane tangent to f(x,y) = 5x²-27*-47-15 at the point (1, - 2) X+ Answer: 9 conds. 7 Question 14 8 9 10 11 15 12 12 A Moving to another question will save this response. R 1 15 n -3 Evaluate the double integral: SS (3x - 5y) da, n , where R ={(x,y)| – 15xs2 and Osys 1). Moving to another question will save this...
sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region. (10pc
(y=2 • A region is bounded by 3 functions: {x = y2 as shown. Clearly x=y construct a double integral to find its area using both dydx and dxdy orders. You do not need to evaluate the integral. 2
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the region R in the ry-plane bounded by the curve y --x? +2x and the line y - x-2, while the top of the solid is bounded by the surface z xy e"
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the...
14 only
13. Use double integrals to find the area inside the curve r = 1 +sin 14. (a) Express f Io ry dy dr as an integral over the triangle D, which is the set of (u. v) where 0s u s 1, 0 ssu (HINT: Find a one-to-one mapping T of D onto the glven region of integration.) (b) Evaluate this integral directly and as an integral over D* 15. Integrate ze+ over the cylinder
13. Use double...
11.1) a) Verify that the function f(x,y) given below is a joint density function for r and y: ſ4.ty if 0 <r<1, 0 <y<1 f(x, y) = { 10 otherwise b) For the probability density function above, find the probability that r is greater than 1/2 and y is less than 1/3. 11.2) For the same probability density function f(x,y) as from Problem #1. Find the expected values of r and y. 11.3) a) Let R= [0,5] x [0,2]. For...
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
1.1. Find the absolute and minimum values of f(x, y) = xy? on the set D= {(x, y)\x² + y si 1.2. Find the extreme values of f(x,y) = x² + y2 + 4x-4y, using the Lagrange multipliers, with the constraint x² + y² 59 1.3. Evaluate the integral - Le*dxdy 1.4. Evaluate the integral L1.** sin(x+ + gydydx 1.5. Find the area of the surface x + y2 +22 - 4 that lies above the plane z = 1....
1. Let R be the region enclosed by the curves y =ra and r = y2 Nole that there is no med to evaluate any integrals in this problem unless you run out of other things to do). a) Find a dy integral for the volume of the solid obtained by rotating R about the r-axis. (Compare with your solution to part f of the last worksheet). b) Find a dx integral for the volume of the solid obtained by...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a) [2 points] First order b) [2 points] Second order c) [6 points] Evaluate the integral using the more convenient order
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
only final answer , no explaining required
Question 13 Find the equation of the plane tangent to f(x,y) = 5x²-27*-47-15 at the point (1, - 2) X+ Answer: 9 conds. 7 Question 14 8 9 10 11 15 12 12 A Moving to another question will save this response. R 1 15 n -3 Evaluate the double integral: SS (3x - 5y) da, n , where R ={(x,y)| – 15xs2 and Osys 1). Moving to another question will save this...
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