Question 1

Find x* on [-4, 4] such that f(x*) equals the average value of f(x) = (x + 4)2 over [-4, 4]. Approximate value to three decimal places.

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& = 21.333
(x + 4)

Question 2

If the velocity of a particle is given by v(t) = 7; [0, 5] the displacement is

Accepted Answer

A)  94.5 
B)  -35 
C)  49 
D)  35 
E)  25 
A)  94.5 
B)  -35 
C)  49 
D)  35 
E)  25

Question 3

Find the area between the curve and the x-axis on the given interval. y = x2 - 4; [-5, 0]

Accepted Answer

A)  27 
B)  5.333 
C)  32.333 
D)  21.667 
E)  16.334 
A)  27 
B)  5.333 
C)  32.333 
D)  21.667 
E)  16.334

Question 4

Evaluate   .

Accepted Answer

u = @#IMG-DLM& , @#IMG-DLM& dt

Question 5

Find the average value of f(x) = x7 + 7 for 0 $\le$  x $\le$  5 and find all values of x* described in the Mean Value Theorem for Integrals.

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& = 9,772.625
To f

Question 6

A particle moves along with a velocity of v(t) = t4 - t8 m/s along an s-axis. Find the distance travelled by the particle during the period 0 $\le$  t $\le$ 4.

Accepted Answer

The answer of A particle moves along with a velocity...

Question 7

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 8

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 9

Answer true or false.   can be easily solved by letting u = x8.

Accepted Answer

A) True 
 B)False

Question 10

For   what is a good choice for u?

Accepted Answer

The answer of For   what is a good...

Question 11

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 12

A particle moves along the s-axis. Use the given information to find the position of the particle. v(t) = 42t6 - 8t + 6; s(1) = 9.

Accepted Answer

s(t) = 6t<

Question 13

Find the displacement of a particle if v(t) = t3; [-1, 0].

Accepted Answer

Question 14

Find the distance an object travels if its velocity is v(t) = t -6t2 in m/s, where 0 $\le$ t $\le$ 1.

Accepted Answer

A)  1.5 
B)  1.5093 
C)  0.0046 
D)  1.5046 
E)  35 
A)  1.5 
B)  1.5093 
C)  0.0046 
D)  1.5046 
E)  35

Question 15

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 16

Find y(x) if   and y(0) = 2 .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Simplify ln(x2e-4x ).

Accepted Answer

Question 18

Find the area under the curve y = x2 - 5 on [2, 4].

Accepted Answer

The answer of Find the area under the curve y...

Question 19

Answer true or false. Using the rectangle method to approximate the area under f(x) = x8 on [-0.5, 0.5] with n = 10 yields 0. (Assume the graph goes through the midpoint of each rectangle.)

Accepted Answer

A) True 
 B)False

Question 20

Find the average value of   for -1 $\le$  x $\le$  5.

Accepted Answer

The answer of Find the average value of  ...

Find x* on [-4, 4] such that f(x*) equals the average value of f(x) = (x + 4)² over [-4, 4]. Approximate value to three decimal places.

If the velocity of a particle is given by v(t) = 7; [0, 5] the displacement is

Find the area between the curve and the x-axis on the given interval. y = x² - 4; [-5, 0]

Evaluate .

Find the average value of f(x) = x⁷ + 7 for 0 $\le$ x $\le$ 5 and find all values of x* described in the Mean Value Theorem for Integrals.

A particle moves along with a velocity of v(t) = t⁴ - t⁸ m/s along an s-axis. Find the distance travelled by the particle during the period 0 $\le$ t $\le$ 4.

Evaluate .

Evaluate .

Answer true or false. can be easily solved by letting u = x⁸.

For what is a good choice for u?

Evaluate .

A particle moves along the s-axis. Use the given information to find the position of the particle. v(t) = 42t⁶ - 8t + 6; s(1) = 9.

Find the displacement of a particle if v(t) = t³; [-1, 0].

Find the distance an object travels if its velocity is v(t) = t -6t² in m/s, where 0 $\le$ t $\le$ 1.

Evaluate .

Find y(x) if and y(0) = 2 .

Simplify ln(x²e^-⁴^x ).

Find the area under the curve y = x² - 5 on [2, 4].

Answer true or false. Using the rectangle method to approximate the area under f(x) = x⁸ on [-0.5, 0.5] with n = 10 yields 0. (Assume the graph goes through the midpoint of each rectangle.)

Find the average value of $Find the average value of for -1 \le x \le 5.$ for -1 $\le$ x $\le$ 5.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 5: Integration

Find x* on [-4, 4] such that f(x*) equals the average value of f(x) = (x + 4)2 over [-4, 4]. Approximate value to three decimal places.

If the velocity of a particle is given by v(t) = 7; [0, 5] the displacement is

Find the area between the curve and the x-axis on the given interval. y = x2 - 4; [-5, 0]

Evaluate .

Find the average value of f(x) = x7 + 7 for 0 ≤\le≤ x ≤\le≤ 5 and find all values of x* described in the Mean Value Theorem for Integrals.

A particle moves along with a velocity of v(t) = t4 - t8 m/s along an s-axis. Find the distance travelled by the particle during the period 0 ≤\le≤ t ≤\le≤ 4.

Evaluate .

Evaluate .

Answer true or false. can be easily solved by letting u = x8.

For what is a good choice for u?

Evaluate .

A particle moves along the s-axis. Use the given information to find the position of the particle. v(t) = 42t6 - 8t + 6; s(1) = 9.

Find the displacement of a particle if v(t) = t3; [-1, 0].

Find the distance an object travels if its velocity is v(t) = t -6t2 in m/s, where 0 ≤\le≤ t ≤\le≤ 1.

Evaluate .

Find y(x) if and y(0) = 2 .

Simplify ln(x2e-4x ).

Find the area under the curve y = x2 - 5 on [2, 4].

Answer true or false. Using the rectangle method to approximate the area under f(x) = x8 on [-0.5, 0.5] with n = 10 yields 0. (Assume the graph goes through the midpoint of each rectangle.)

Find the average value of for -1 ≤\le≤ x ≤\le≤ 5.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find x* on [-4, 4] such that f(x*) equals the average value of f(x) = (x + 4)² over [-4, 4]. Approximate value to three decimal places.

Find the area between the curve and the x-axis on the given interval. y = x² - 4; [-5, 0]

Find the average value of f(x) = x⁷ + 7 for 0 $\le$ x $\le$ 5 and find all values of x* described in the Mean Value Theorem for Integrals.

A particle moves along with a velocity of v(t) = t⁴ - t⁸ m/s along an s-axis. Find the distance travelled by the particle during the period 0 $\le$ t $\le$ 4.

Answer true or false. can be easily solved by letting u = x⁸.

A particle moves along the s-axis. Use the given information to find the position of the particle. v(t) = 42t⁶ - 8t + 6; s(1) = 9.

Find the displacement of a particle if v(t) = t³; [-1, 0].

Find the distance an object travels if its velocity is v(t) = t -6t² in m/s, where 0 $\le$ t $\le$ 1.

Simplify ln(x²e^-⁴^x ).

Find the area under the curve y = x² - 5 on [2, 4].

Answer true or false. Using the rectangle method to approximate the area under f(x) = x⁸ on [-0.5, 0.5] with n = 10 yields 0. (Assume the graph goes through the midpoint of each rectangle.)

Find the average value of $Find the average value of for -1 \le x \le 5.$ for -1 $\le$ x $\le$ 5.