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![1972 I cosol (5)3-(133) do 172 I. ${(253)-1] ) cosodo I $( 253.-) [ Sino) I= 5 ( 252-13 [ Bin (1/2)- sino). Ź [ 252-1] [1-0)](http://img.homeworklib.com/questions/c361ba50-4094-11eb-ade4-39a1465237b2.png?x-oss-process=image/resize,w_560)
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4. Evaluate ſfx da, where D is the region in the first quadrant that lies between...
7. (5 points) Evaluate S SpydA, where D is the region in the first quadrant bounded...
7. (5 points) Evaluate S SpydA, where D is the region in the first quadrant bounded by the parabolas r = y2 and x = 8 – y?.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the...
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
2. Let f(x,y) = e In(y) and let R be the region in the first quadrant...
2. Let f(x,y) = e In(y) and let R be the region in the first quadrant of the plane that lies above r = = In(y) from y=1 to y = 2. (a) Sketch the region R in the plane. (b) Evaluate SSR f(x,y) dA.
Use the given transformation to evaluate the integral. 10xy da, where is the region in the...
Use the given transformation to evaluate the integral. 10xy da, where is the region in the first quadrant bounded by the lines y = 1x and y = 3x and the hyperbolas xy - 3 and xy = 3; xu/v, y v
(1) Evaluate S SIS "Jo dzdydi B. Evaluate JJ y dA where D is the region...
(1) Evaluate S SIS "Jo dzdydi B. Evaluate JJ y dA where D is the region bounded by xay and y = 2 - X.
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x,...
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
4. (a) Let D be the region located in the first quadrant of R2 between the...
4. (a) Let D be the region located in the first quadrant of R2 between the two circles of radii 1 and 4 centered on the origin. Evaluate ((a2 2) dady sin D 5 marks (b) Consider the thin disk centered on the origin in R2 of radius 1. Suppose it is made of a material with mass density function p(г, у) exp 1 x22 in grams per units of area. Show that the mass of the disk does not...
2. Set up and evaluate the volume integral for the region whose base D lies in...
2. Set up and evaluate the volume integral for the region whose base D lies in the first quadrant in the xy plane and whose top is bounded by x + y + z = 4. 3. Find the volume that is enclosed by both the cone z = x2 + y2 and the sphere x2 + y2 + z = 2
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where...
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the...
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the circle x2 +y2 = 4 and the lines x = 0 and y = 0. The density function of the lamina is equal to p(x, y) = V x2 + y2. Use the double integral formula in polar coordinates, S/ s(8,y)dx= $." \* fcr cos 6,r sin Øyrar] de, Ja [ Ꭱ . to calculate (1) the mass of the lamina, m = SSP(x,y)...
7. (5 points) Evaluate S SpydA, where D is the region in the first quadrant bounded by the parabolas r = y2 and x = 8 – y?.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
2. Let f(x,y) = e In(y) and let R be the region in the first quadrant of the plane that lies above r = = In(y) from y=1 to y = 2. (a) Sketch the region R in the plane. (b) Evaluate SSR f(x,y) dA.
Use the given transformation to evaluate the integral. 10xy da, where is the region in the first quadrant bounded by the lines y = 1x and y = 3x and the hyperbolas xy - 3 and xy = 3; xu/v, y v
(1) Evaluate S SIS "Jo dzdydi B. Evaluate JJ y dA where D is the region bounded by xay and y = 2 - X.
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
4. (a) Let D be the region located in the first quadrant of R2 between the two circles of radii 1 and 4 centered on the origin. Evaluate ((a2 2) dady sin D 5 marks (b) Consider the thin disk centered on the origin in R2 of radius 1. Suppose it is made of a material with mass density function p(г, у) exp 1 x22 in grams per units of area. Show that the mass of the disk does not...
2. Set up and evaluate the volume integral for the region whose base D lies in the first quadrant in the xy plane and whose top is bounded by x + y + z = 4. 3. Find the volume that is enclosed by both the cone z = x2 + y2 and the sphere x2 + y2 + z = 2
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the circle x2 +y2 = 4 and the lines x = 0 and y = 0. The density function of the lamina is equal to p(x, y) = V x2 + y2. Use the double integral formula in polar coordinates, S/ s(8,y)dx= $." \* fcr cos 6,r sin Øyrar] de, Ja [ Ꭱ . to calculate (1) the mass of the lamina, m = SSP(x,y)...
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