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Calculus 4-R Unit 4 Integration Review Problems
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Evaluate 6 1
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Review Problems -2 1 Evaluate 2
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Review Problems Find the average value of f(x) = 3x 2 - 2 on the interval [0, 2]. 2 Find the average value of y = x 3 over the interval [0, 2]. 2 3
![Review Problems Find the average value of f(x) = 3x on the interval [0, 2].](http://images.slideplayer.com/39/11003999/slides/slide_4.jpg "2 Find the average value of y = x 3 over the interval [0, 2]")
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Review Problems Find the area of the region bounded by y = (x - 1) 2 + 1, the x-axis, x = -1, and x = 2. 6 Find the value of c guaranteed by the Mean Value Theorem for Integrals for on the interval [1, 4]. 2 4
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Review Problems Consider Find and 5
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Review Problems Evaluate 6
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Review Problems Evaluate 7
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Review Problems Evaluate 8
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Review Problems Evaluate 9
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Review Problems Evaluate 10
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Review Problems Find an expression in a and b for the value of the definite integral 11
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Review Problems Consider the integral, Determine new upper and lower limits of integration using the substitution u = 4x 2 - 3. Upper, 97; lower, 5 Use the Trapezoidal Rule, with n = 4, to approximate -53.59 12
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Review Problems Use the Trapezoidal Rule, with n = 4, to approximate the area of the region bounded by the graphs of y = sin x and y = 0 on the interval [0, π ]. 13
![Review Problems Use the Trapezoidal Rule, with n = 4, to approximate the area of the region bounded by the graphs of y = sin x and y = 0 on the interval [0, π ].](http://images.slideplayer.com/39/11003999/slides/slide_14.jpg "13.")
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Review Problems Find the function, y = f(x), if and f(1) = 3 y = x 2 - x + 3 Find y = f(x) if and f(0) = 2. 14
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Review Problems Evaluate 15
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Review Problems Evaluate 16
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Review Problems Use the properties of sigma notation and the summation formulas to evaluate the given sums: 530 625 17
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Review Problems Find the limit of s(n) as 4 1 18
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Review Problems Find the limit: 19
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Review Problems LetFind the limit of s(n) as LetFind the limit of s(n) as 4 20
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Review Problems Write the definite integral that represents the area of the shaded region? 21
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Review Problems Write the definite integral for the area of the region bounded by the graphs of y = 9 - x 2 and y = 0. Write the definite integral for the area of the region lying in the upper half of the ellipse given by 4x 2 + y 2 = 4. 22
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Review Problems Sketch the region whose area is indicated by the integral: 23
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Review Problems Given that Find 10 Given that Find 6 24
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Review Problems Given that Find Given that 11 8 25
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Review Problems Consider Find and Consider Find 26
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Review Problems Evaluate (2x 2 + 5) 2 Find the average value of y = x 3 over the interval [0,2] 2 27
![Review Problems Evaluate (2x 2 + 5) 2 Find the average value of y = x 3 over the interval [0,2] 2 27](http://images.slideplayer.com/39/11003999/slides/slide_28.jpg "Review Problems Evaluate (2x 2 + 5) 2 Find the average value of y = x 3 over the interval [0,2] 2 27")
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Review Problems Use the Fundamental Theorem of Calculus to evaluate: 1 28
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Review Problems Evaluate 29
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Review Problems Evaluate 30
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Review Problems Evaluate 31
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Review Problems Evaluate 4 32
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Review Problems Use the Trapezoidal Rule, with n = 4, to approximate -53.59 Use the Trapezoidal Rule, with n = 4, to approximate -10.00 33
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Review Problems Consider the region bounded by the x-axis, the function x = 1, and x = -1 Use the Trapezoidal Rule, with n = 4, to approximate the area of the region. (Round the answer to three decimal places.) 1.852 34
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Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 4 1 19. 20. 6 -2 1 22 6 2 Upper, 97; lower, 5 -53.59 y = x 2 - x + 3 530625 4
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Answers 21. 22. 23. graph 24. 10 6 25. 8 11 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. (2x 2 + 5) 2 2 1 4 -53.59-10.00 1.852
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