Deck 5: Antiderivatives and Indefinite Integration

Question 1

the indefinite integral

Answer 1

A

Question 2

the indefinite integral and check the result by differentiation.

Answer 2

E

Question 3

ball is thrown vertically upwards from a height of ft with an initial velocity of

Answer 3

E

Question 4

the indefinite integral

Question 5

the indefinite integral

Question 6

the indefinite integral

Question 7

maker of an automobile advertises that it takes

Question 8

the indefinite integral

Question 9

height above the ground of an object thrown upward from a point feet above the ground with an initial velocity of feet per second is given by the function

Question 10

the indefinite integral

Question 11

Solve the differential equation.

Question 12

Solve the differential equation.

Question 13

the general solution of the differential equation below and check the result by differentiation.

Question 14

maker of an automobile advertises that it takes kilometers per hour to kilometers per hour. Assuming constant acceleration, compute the acceleration in meters per second per second. Round your answer to three decimal places.

Question 15

the general solution of the differential equation below and check the result by differentiation.

Question 16

Solve the differential equation.

Question 17

height above the ground of an object thrown upward from a point feet above the ground with an initial velocity of feet per second is given by the function

Question 18

the indefinite integral

Question 19

the indefinite integral

Question 20

the sum given below.

Question 21

the sum given below.

Question 22

the summation formulas to rewrite the expression summation notation.

Question 23

the properties of summation and Theorem 5.2 to evaluate the sum.

Question 24

the limit of

Question 25

Evaluate the following definite integral by the limit definition.

Question 26

Evaluate the following definite integral by the limit definition.

Question 27

diagram below shows upper and lower sums for the function using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals.

Question 28

the limit process to find the area of the region between the graph of the function

Question 29

left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function your answer to the nearest integer.

Question 30

the properties of summation and Theorem 5.2 to evaluate the sum.

Question 31

sigma notation to write the sum

Question 32

the properties of summation and Theorem 5.2 to evaluate the sum.

Question 33

the sum given below.

Question 34

Evaluate the following definite integral by the limit definition.

Question 35

left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval answer to four decimal places.

A)0.0419
B)0.1319
C)0.1219
D)0.0819
E)0.0119

Question 36

Question 37

Write the following limit as a definite integral on the interval [2 , 5], where ci is any point in the ith subinterval.

Question 38

the properties of summation and Theorem 5.2 to evaluate the sum.

Question 39

the properties of summation and Theorem 5.2 to evaluate the sum.

Question 40

the limit.

Question 41

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Question 42

Evaluate the definite integral

Question 43

Evaluate the integral.

Question 44

Write the limit

Question 45

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Question 46

Evaluate the integral.

Question 47

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

Question 48

Write the limit where ci is any point in the subinterval.

Question 49

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Question 50

Write the following limit as a definite integral on the interval point in the

Question 51

Evaluate the definite integral of a function your results.

Question 52

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

Question 53

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Question 54

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Question 55

graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

Question 56

graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

Question 57

graph of f consists of line segments, as shown in the figure. Evaluate the definite

Question 58

Evaluate the integral.

Question 59

Evaluate the integral.

Question 60

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

A)148.5
B)12
C)79.5
D)159
E)15

Question 61

Determine the area of the given region.

Question 62

the area of the region bounded by the graphs of the equations

Question 63

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

Question 64

the indefinite integral

Question 65

Solve the differential equation.

Question 66

Question 67

Evaluate the definite integral of the trig function. Use a graphing utility to verify your results.

Question 68

the indefinite integral of the following function and check the result by differentiation.

Question 69

Question 70

the indefinite integral of the following function and check the result by differentiation.

Question 71

Question 72

Question 73

Question 74

Solve the differential equation.

Question 75

(in newtons) of a hydraulic cylinder in a press is proportional to the

Question 76

Determine the area of the given region.

Question 77

Question 78

Question 79

the indefinite integral of the following function and check the result by differentiation.

Question 80

Evaluate the definite integral of the function. Use a graphing utility to verify your results.