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Exam 4: Integrals

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Exam 1: Functions and Limits117 Questionsadd course
Exam 2: Derivatives151 Questionsadd course
Exam 3: Applications of Differentiation153 Questionsadd course
Exam 4: Integrals95 Questionsadd course
Exam 5: Applications of Integration120 Questionsadd course
Exam 6: Inverse Functions127 Questionsadd course
Exam 7: Techniques of Integration124 Questionsadd course
Exam 8: Further Applications of Integration86 Questionsadd course
Exam 9: Differential Equations67 Questionsadd course
Exam 10: Parametric Equations and Polar Coordinates72 Questionsadd course
Exam 11: Infinite Sequences and Series158 Questionsadd course
Exam 12: Vectors and the Geometry of Space60 Questionsadd course
Exam 13: Vector Functions93 Questionsadd course
Exam 14: Partial Derivatives132 Questionsadd course
Exam 15: Multiple Integrals124 Questionsadd course
Exam 16: Vector Calculus137 Questionsadd course
Exam 17: Second-Order Differential Equations63 Questionsadd course
Exam 18: Final Exam44 Questionsadd course
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The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.5 4.4 6.5 9.4 12.2 16.8 2.5 4.4 6.5 9.4 12.2 16.8

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Question 61

Evaluate Evaluate by interpreting it in terms of areas. by interpreting it in terms of areas.

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Question 62

Express the sum as a single integral in the form Express the sum as a single integral in the form . . Express the sum as a single integral in the form .

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Question 63

The area of the region that lies to the right of the y-axis and to the left of the parabola The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral . Find the area. (the shaded region in the figure) is given by the integral The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral . Find the area. . Find the area. The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral . Find the area.

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Question 64

Evaluate the integral. Evaluate the integral.

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Question 65

Find the indefinite integral. Find the indefinite integral.

(Multiple Choice)
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Question 66

Find the limit. Find the limit.

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Question 67

Find the derivative of the function. Find the derivative of the function.

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Question 68

If If , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints. , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

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Question 69

Evaluate by interpreting it in terms of areas. Evaluate by interpreting it in terms of areas.

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Question 70

Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically. Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically. Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically.

(Multiple Choice)
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Question 71

You are given function f defined on an interval [a, b], the number n of subintervals of equal length You are given function f defined on an interval [a, b], the number n of subintervals of equal length , and the evaluation points c<sub>k</sub> in . (a) Sketch the graph of f and the rectangles associated with the Riemann sum for f on [a, b], and (b) find the Riemann sum. , c<sub>k</sub> is the right endpoint , and the evaluation points ck in You are given function f defined on an interval [a, b], the number n of subintervals of equal length , and the evaluation points c<sub>k</sub> in . (a) Sketch the graph of f and the rectangles associated with the Riemann sum for f on [a, b], and (b) find the Riemann sum. , c<sub>k</sub> is the right endpoint . (a) Sketch the graph of f and the rectangles associated with the Riemann sum for f on [a, b], and (b) find the Riemann sum. You are given function f defined on an interval [a, b], the number n of subintervals of equal length , and the evaluation points c<sub>k</sub> in . (a) Sketch the graph of f and the rectangles associated with the Riemann sum for f on [a, b], and (b) find the Riemann sum. , c<sub>k</sub> is the right endpoint , ck is the right endpoint

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Question 72

Find the indefinite integral. Find the indefinite integral.

(Multiple Choice)
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Question 73

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 0 0 60 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 10 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 70 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 20 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 80 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 30 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 90 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 40 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 100 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0 60 10 70 20 80 30 90 40 100 50

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Question 74

Evaluate the integral. Evaluate the integral.

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Question 75

Approximate the area under the curve Approximate the area under the curve from using approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth. from Approximate the area under the curve from using approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth. using Approximate the area under the curve from using approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth. approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth.

(Multiple Choice)
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Question 76

Find the general indefinite integral. Find the general indefinite integral.

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Question 77

By reading values from the given graph of f , use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of f . By reading values from the given graph of f , use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of f .

(Short Answer)
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Question 78

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 0 0 60 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 10 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 70 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 20 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 80 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 30 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 90 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 40 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 100 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50 50 The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. Round your answer to the nearest tenth. 0 0 60 10 70 20 80 30 90 40 100 50

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Question 79

Evaluate the integral. Evaluate the integral.

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Question 80
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