Deck 4: Section 6: Integration

Question 1

Use the error formula to estimate the error in approximating the integral with using Simpson's Rule. Round your answer to six decimal places.

A) 0.007084
B) 0.141676
C) 0.004723
D) 0.003936
E) 0.002530

Answer 1

0.003936

Question 2

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

A) The Trapezoidal rule gives 16.3400 and Simpson's rule gives .
B) The Trapezoidal rule gives 16.3400 and Simpson's rule gives .
C) The Trapezoidal rule gives and Simpson's rule gives .
D) The Trapezoidal rule gives and Simpson's rule gives .
E) The Trapezoidal rule gives and Simpson's rule gives .

Answer 2

The Trapezoidal rule gives and Simpson's rule gives .

Question 3

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

A) The Trapezoidal rule gives and Simpson's rule gives .
B) The Trapezoidal rule gives 1.3973 and Simpson's rule gives .
C) The Trapezoidal rule gives and Simpson's rule gives .
D) The Trapezoidal rule gives 1.3973 and Simpson's rule gives .
E) The Trapezoidal rule gives and Simpson's rule gives .

Answer 3

The Trapezoidal rule gives and Simpson's rule gives .

Question 4

Use the Trapezoidal Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

A) -8.0654
B) -4.0327
C) -2.0164
D) -1.0082
E) -0.5041

Question 5

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places.

A) 3.501
B) 3.581
C) 3.901
D) 3.529
E) 3.171

Question 6

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

A) The Trapezoidal rule gives and Simpson's rule gives .
B) The Trapezoidal rule gives and Simpson's rule gives .
C) The Trapezoidal rule gives and Simpson's rule gives .
D) The Trapezoidal rule gives 1.366795 and Simpson's rule gives .
E) The Trapezoidal rule gives 1.366795 and Simpson's rule gives .

Question 7

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

A) The Trapezoidal rule gives 43.377044 and Simpson's rule gives .
B) The Trapezoidal rule gives and Simpson's rule gives .
C) The Trapezoidal rule gives 43.377044 and Simpson's rule gives .
D) The Trapezoidal rule gives and Simpson's rule gives .
E) The Trapezoidal rule gives and Simpson's rule gives .

Question 8

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

A) 10
B) 16
C) 6
D) 8
E) 13

Question 9

Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

A)
B)
C)
D)
E)

Question 10

Use Simpson's Rule with to approximate using the equation . Round your answer to five decimal places.

A) 3.14159
B) 3.13595
C) 3.14723
D) 3.14381
E) 3.13937

Question 11

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

A) The Trapezoidal rule gives 0.7100 and Simpson's rule gives .
B) The Trapezoidal rule gives and Simpson's rule gives .
C) The Trapezoidal rule gives 0.7100 and Simpson's rule gives .
D) The Trapezoidal rule gives and Simpson's rule gives .
E) The Trapezoidal rule gives and Simpson's rule gives .

Question 12

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative.

A) 208
B) 189
C) 196
D) 201
E) 188

Question 13

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

A) 48
B) 8
C) 11
D) 14
E) 19

Question 14

Use the Trapezoid Rule to approximate the value of the definite integral wth . Round your answer to four decimal places.

A)
B)
C)
D)
E)

Question 15

Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

A) 2.9784
B) 3.0627
C) 8.0100
D) 10.6800
E) 2.6700

Question 16

Estimate the error in using (a) the Trapezoidal Rule and (b) Simpson's Rule with when approximating the following integral.

A) The error for the Trapezoidal Rule is 0.0051 and for Simpson's Rule it is 0.0013.
B) The error for the Trapezoidal Rule is 0.0000 and for Simpson's Rule it is 0.0200.
C) The error for the Trapezoidal Rule is 0.0204 and for Simpson's Rule it is 0.0200.
D) The error for the Trapezoidal Rule is 0.0204 and for Simpson's Rule it is 0.0000.
E) The error for the Trapezoidal Rule is 0.0000 and for Simpson's Rule it is 0.0000.

Question 17

Use the error formula to estimate the error in approximating the integral with using Trapezoidal Rule.

A) 3
B) 1
C) 6
D) 0
E) 9

Question 18

Find the smallest n such that the error estimate from the error formula in the approximation of the definite integral is less than 0.00001 using the Trapezoidal Rule.

A) 49
B) 26
C) 73
D) 30
E) 15