Evaluate the integral by changing to polar coordinates

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Presentation transcript:

Evaluate the integral by changing to polar coordinates Evaluate the integral by changing to polar coordinates. {image} where D is the region bounded by the semicircle {image} and the y-axis. 1. {image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Use polar coordinates to find the volume of the sphere of radius 7 Use polar coordinates to find the volume of the sphere of radius 7. Select the correct answer. The choices are rounded to the nearest hundredth. 1. {image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Use polar coordinates to find the volume of the solid inside the cylinder {image} and the ellipsoid {image} Select the correct answer. The choices are rounded to the nearest hundredth. 1. {image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Evaluate the iterated integral by converting to polar coordinates Evaluate the iterated integral by converting to polar coordinates. {image} Select the correct answer. The choices are rounded to the nearest hundredth. 1. {image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

An agricultural sprinkler distributes water in a circular pattern of radius 100 ft. It supplies water to a depth of {image} feet per hour at a distance of r feet from the sprinkler. What is the total amount of water supplied per hour to the region inside the circle of radius 65 feet centered at the sprinkler? Select the correct answer. The choices are rounded to the nearest thousandth. 1. {image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50