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
1