Homework Answers
In (1) we need to find the limits of integration, which can be simply found by knowing upper and lower bounds of x and y
Since x is in [a,b] so we need to go along X-axis from a to b
similarly along y-axis c to d, in (2) all this work is already
done... and dA=dx.dy represents small area element... in short
there is no difference except that in (2) half of work is already
done.
Add Answer to:
Let
R= [a,b] x [c,d]. Explain the difference between these two
notations for a double integral....
Evaluate the double integral integral | | =+ wy? + rʻydA R where R= {(x,y) 1<x<2,1...
Evaluate the double integral integral | | =+ wy? + rʻydA R where R= {(x,y) 1<x<2,1 <y<2} Double Integral Plot of integrand and Region R 300- 1] 1] 200 1] 100 0 -100 /1) /1) 0/1) 0/1) (0/1) 3/19 ersion -200 -300 101234 This plot is an example of the function over region R. The region and function identified in your problem slightly different Preview Answer Round your answer to four decimal places
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r,...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Let R = [0,2] x [0,6]. Approximate the double integral of (x^2-y^2)dA using a Riemann sum...
Let R = [0,2] x [0,6]. Approximate the double integral of
(x^2-y^2)dA using a Riemann sum with 3 congruent squares with
integer sides and taking (xi*,yj*) to be the center of each
rectangle.
z 2 of each sectarg
f(x,y)= x^4 + 2x^2 y^2 + y^4 Double integral D= (r, theta) 3<=r <= 4 pi...
f(x,y)= x^4 + 2x^2 y^2 + y^4 Double integral D= (r, theta) 3<=r <= 4 pi / 3 <= theta <= pi Evaluate double integral over polar rectangular region 3367 pi / 18 is final answer
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image...
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working.
(7) Let 0くa 〈 b 〈 c 〈...
(7) Let 0 < a < b < c 〈 d for a,b,c,de R. Consider the set and let D be the region in the r-y plance that is...
(7) Let 0 < a < b < c 〈 d for a,b,c,de R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation ( d -bc > 0. a) Sketch D in the x-y plane for the case a -bc< (a) Sketch D in the r-y plane for the case ad 0. (c) Calculate the area of D. Show all working.
(7) Let 0
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus c) Use d...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus c) Use double integral to get the surface area of this torus.
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the...
Please step by step double integral to find the area of the region R enclosed between...
Please step by step double integral to find the area of the region R enclosed between the line y = x and the parabola y = x-
Let B C R" be any set. Define C = {x € R" | d(x,y) <...
Let B C R" be any set. Define C = {x € R" | d(x,y) < 1 for some y E B) Show that C is open.
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use double integral to get the surface area of this torus. d) Let's say you have a circle on the xy-axis with the centre (a, a) and radius b as shown in the figure below, where a > b....
Evaluate the double integral integral | | =+ wy? + rʻydA R where R= {(x,y) 1<x<2,1 <y<2} Double Integral Plot of integrand and Region R 300- 1] 1] 200 1] 100 0 -100 /1) /1) 0/1) 0/1) (0/1) 3/19 ersion -200 -300 101234 This plot is an example of the function over region R. The region and function identified in your problem slightly different Preview Answer Round your answer to four decimal places
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Let R = [0,2] x [0,6]. Approximate the double integral of
(x^2-y^2)dA using a Riemann sum with 3 congruent squares with
integer sides and taking (xi*,yj*) to be the center of each
rectangle.
z 2 of each sectarg
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working.
(7) Let 0くa 〈 b 〈 c 〈...
(7) Let 0 < a < b < c 〈 d for a,b,c,de R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation ( d -bc > 0. a) Sketch D in the x-y plane for the case a -bc< (a) Sketch D in the r-y plane for the case ad 0. (c) Calculate the area of D. Show all working.
(7) Let 0
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus c) Use double integral to get the surface area of this torus.
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the...
Please step by step double integral to find the area of the region R enclosed between the line y = x and the parabola y = x-
Let B C R" be any set. Define C = {x € R" | d(x,y) < 1 for some y E B) Show that C is open.
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use double integral to get the surface area of this torus. d) Let's say you have a circle on the xy-axis with the centre (a, a) and radius b as shown in the figure below, where a > b....
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