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CHAPTER 5

Integration SECTION 5.1 1. f (x) = 4x; [0, 1] Use the rectangle method to approximate the area using 4 rectangles. A. 2

B. 1

C. 1.5

D. 1.75

2. f (x) = 10 + x; [0, 2] Use the rectangle method to approximate the area using 4 rectangles. A. 10.625 3. f (x) =

B. 10.375

C. 11.000

D. 10.750

1 + x + 2; [0, 1] Use the rectangle method to approximate the area using 4 rectangles.

A. 3.166

B. 3.250

C. 3.500

D. 3.141

4. f (x) = 6x − 2 [0.5, 4.5]. Use the rectangle method to approximate the area using 4 rectangles. A. 0

B. 52

C. 60

D. 100

5. f (x) = x3 [0.5, 4.5]. Use the rectangle method to approximate the area using 4 rectangles. A. 117

B. 130

C. 150

D. 160

6. f (x) = x3 + 5 [0.5, 4.5]. Use the rectangle method to approximate the area using 4 rectangles. A. 133

B. 146

C. 166

D. 176

7. Answer true or false: Using the rectangle method to approximate the area under f (x) = x4 on [−2.5, 2.5] with n = 10 yields 100. 8. Answer true or false: Using the rectangle method to approximate the area under f (x) = x3 on [0.25, 2.25] with n = 4 yields 11.25. 9. Answer true or false: Using the rectangle method to approximate the area under f (x) = 2x4 on [−2, 0] with n = 4 yields 45. 10. Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f (x) = 4 and the interval [a, x] = [2, x]. A. 4(x − 2)

B. 4(x + 2)

C. 4x

D. 4

11. Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f (x) = 8 and the interval [a, x] = [−3, x]. A. 8(x − 2)

B. 8(x + 3)

C. 8x

D. 8

12. Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f (x) = x + 5 and the interval [a, x] = [−5, x]. A.

1 (x + 5)(x − 3) 2

B.

1 (x + 5)2 2

C.

1 (x + 5)(x + 3) 2

D.

1 2 x 2

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