WebAssign Lesson 1-2a Area Between Curves (Homework)

Transcription

1 WebAssign Lesson 1-2a Area Between Curves (Homework) Current Score : / 30 Due : Thursday, June :00 AM MDT Jaimos Skriletz Math 175, section 31, Summer Instructor: Jaimos Skriletz 1. /3 points Follow the steps find the area bounded by the curve y = x(4 x) and the x-axis as shown In this problem steps 1 and 2 (graphing the region and drawing the sample rectangle) have been provided for you. Use the graph and given slice to find the area: 3. Find the small amount of area, da, of each slice at the point x. 4. Set up the definite integral to sum up the area's of the little slices: x=b b A = x=a a Were the bounds of integration are 5. Evaluate the above definite integral to find the total area.

2 A = 2. /3 points Follow the steps find the area bounded the curves shown y = 2 + x x 2, y = x 2 and the y-axis as In this problem steps 1 and 2 (graphing the region and drawing the sample rectangle) have been provided for you. Use the graph and given slice to find the area: 3. Find the height (h), width (w), and area (da) of each rectangle slice in terms of the variable x. h = w = 4. Find the bonds of integration by solving the equation: 2 + x x 2 = x 2 (lower bound)

3 (upper bound) 5. Evaluate the definite integral to find the total area. b A = a

4 3. /3 points Follow the steps find the area bounded the curves y = and y = x 3 x as shown In this problem steps 1 and 2 (graphing the region and drawing the sample rectangle) have been provided for you. Use the graph and given slice to find the area: 3. Find the area element of each rectangle slice, da, in terms of the variable x. 4. Find the bonds of integration by solving the equation: x = x 3 (lower bound) (upper bound) 5. Evaluate the definite integral to find the total area. b A = a

5 4. /3 points Find the area of the region enclosed by the graphs of f(x) = x and g(x) = 2x Sketch the region in question on your own paper. 2. Slice the region into rectangles along the x-axis and draw a sample rectangle of width dx. WebAssign cannot check your graphs, show your graph to your instructor to check you have drawn the proper region and area slice. 3. Find the little bit of area, da of the slice. 4. Find the bounds of integration and set up the definite integral. x=b A = da x=a Where the bounds of integration are 5. Evaluate the definite integral to find the area. (Enter in the exact value.) Are

6 5. /3 points Find the area of the region enclosed by the graphs of y = sin(x) and y = cos(x) on the interval π, 5π Sketch the region in question on your own paper. 2. Slice the region into rectangles along the x-axis and draw a sample rectangle of width dx. WebAssign cannot check your graphs, show your graph to your instructor to check you have drawn the proper region and area slice. 3. Find the little bit of area, da of the slice. 4. Find the bounds of integration and set up the definite integral. x=b A = da x=a Where the bounds of integration are 5. Evaluate the definite integral to find the area. (Enter in the exact value.) Are 6. /4 points Follow the steps to find the area bounded the curves y = x 3 7x x the x axis as shown

7 To find this area you need to find the two areas 1. Find area A 1 as follows A 1 and A 2 separately Split the area into rectangles then find the area ( da 1 ) of each rectangle in terms of the variable x. da 1 = Find the bonds of integration by solving the equation: (lower bound) (upper bound) Evaluate the definite integral to find the total area. b A 1 = da 1 = a 2. Find area A 2 as follows Split the area into rectangles then find the area ( da 2 ) of each rectangle in terms of the variable x. da 2 = Find the bonds of integration by solving the equation:

8 (lower bound) (upper bound) Evaluate the definite integral to find the total area. b A 2 = da 2 = a 3. What is the total area (give an exact answer)? 7. /2 points Find the area bounded by the curves shown y = sin(x) and y = sin(2x) between x = 0 and x = π as What is the total area (enter in an exact answer): A = 8. /3 points Follow the steps find the area bounded the curves x = 2y 2 and x = 12 y 2 as shown

9 In this problem steps 1 and 2 (graphing the region and drawing the sample rectangle) have been provided for you. Use the graph and given slice to find the area: 3. Find the area of each slice along y-axis by finding the height (h), length (l), and area da in terms of the variable y h = l = 4. Find the bonds of integration: (lower bound) (upper bound) 5. Evaluate the definite integral to find the total area. y=b A = y=a

10 9. /2 pointsrogac alcet Find the area of the region lying to the right of x = y y + 26 and to the left of x = 3y /2 pointsrogac alcet Find the area between the graphs x = sin(9y) and x = 1 cos(9y) over the interval 0 y π 18 in figure below.

11 11. /2 pointsrogac alcet Find the area between the graphs x = sin(3y) and x = 1 cos(3y) over the interval π 6 y π 6 in figure below.