Exam 4: Integrals
Exam 1: Functions and Limits117 Questions
Exam 2: Derivatives151 Questions
Exam 3: Applications of Differentiation153 Questions
Exam 4: Integrals95 Questions
Exam 5: Applications of Integration120 Questions
Exam 6: Inverse Functions127 Questions
Exam 7: Techniques of Integration124 Questions
Exam 8: Further Applications of Integration86 Questions
Exam 9: Differential Equations67 Questions
Exam 10: Parametric Equations and Polar Coordinates72 Questions
Exam 11: Infinite Sequences and Series158 Questions
Exam 12: Vectors and the Geometry of Space60 Questions
Exam 13: Vector Functions93 Questions
Exam 14: Partial Derivatives132 Questions
Exam 15: Multiple Integrals124 Questions
Exam 16: Vector Calculus137 Questions
Exam 17: Second-Order Differential Equations63 Questions
Exam 18: Final Exam44 Questions
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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.
2.5
4.4
6.5
9.4
12.2
16.8
(Essay)
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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. 
(Multiple Choice)
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If
, find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.
(Essay)
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Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically.

(Multiple Choice)
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You are given function f defined on an interval [a, b], the number n of subintervals of equal length
, and the evaluation points ck 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.
, ck is the right endpoint
(Essay)
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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.
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(Multiple Choice)
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Approximate the area under the curve
from
using
approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth.
(Multiple Choice)
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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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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.
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0
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10
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50 
(Short Answer)
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