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Evaluate (*V19x2 + 19y2 dA, where D is the shaded region enclosed by the lemniscate curve...
Find the area of the shaded region bounded by y = 2x and y = xV49...
Find the area of the shaded region bounded by y = 2x and y = xV49 – x2 in the figure. 2. (Give an exact answer. Use symbolic notation and fractions where needed.)
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.
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 3...
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 3 + x2 + y2, the cylinder x2 + y2 = 6, and the xy-plane. e dy
Q4: Use polar coordinates to evaluate x2 - y2 dA, where R is the region in...
Q4: Use polar coordinates to evaluate x2 - y2 dA, where R is the region in the first V9- quadrant within the circle x2 + y2-9.
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
(a) Find the volume of the region bounded above by the sphere x2 +y2 +z225 and below by the plane z - 4 by using cylind...
(a) Find the volume of the region bounded above by the sphere x2 +y2 +z225 and below by the plane z - 4 by using cylindrical coordinates Evaluate the integral (b) 2x2dA ER where R is the region bounded by the square - 2
3. Draw the region D and evaluate the double integral using polar coordinates. (a) SI x...
3. Draw the region D and evaluate the double integral using polar coordinates. (a) SI x + y dA, x2 + y2 D= {(x, y)| x2 + y2 < 1, x + y > 1} D (b) ſ sin(x2 + y2)dA, D is in the third quadrant enclosed by m2 + y2 = 71, x2 + y2 = 27, y=x, y= V3x.
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...
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region...
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region 1 5x2 + y2 549. 1.080
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
Find the area of the shaded region bounded by y = 2x and y = xV49 – x2 in the figure. 2. (Give an exact answer. Use symbolic notation and fractions where needed.)
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.
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 3 + x2 + y2, the cylinder x2 + y2 = 6, and the xy-plane. e dy
Q4: Use polar coordinates to evaluate x2 - y2 dA, where R is the region in the first V9- quadrant within the circle x2 + y2-9.
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
(a) Find the volume of the region bounded above by the sphere x2 +y2 +z225 and below by the plane z - 4 by using cylindrical coordinates Evaluate the integral (b) 2x2dA ER where R is the region bounded by the square - 2
3. Draw the region D and evaluate the double integral using polar coordinates. (a) SI x + y dA, x2 + y2 D= {(x, y)| x2 + y2 < 1, x + y > 1} D (b) ſ sin(x2 + y2)dA, D is in the third quadrant enclosed by m2 + y2 = 71, x2 + y2 = 27, y=x, y= V3x.
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...
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region 1 5x2 + y2 549. 1.080
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
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