Question 1

Find the displacement of a particle if v(t) = sin t; [0,  $\pi$].

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  2 $\pi$ 
E)   $\pi$

Question 2

Find the displacement of an object if its velocity is v(t) = t4 - 2t in m/s, where 0 $\le$ t $\le$2.

Accepted Answer

A)  8.4 
B)  6.4 
C)  12 
D)  -0.8 
E)  2.4

Question 3

Find the distance an object travels if its velocity is v(t) = 4t³ - 4t in m/s, where 0 $\le$ t $\le$ 4.

Accepted Answer

The answer of Find the distance an object travels if...

Question 4

Evaluate  .

Accepted Answer

The answer of Evaluate  ....

Question 5

Evaluate

Accepted Answer

The answer of Evaluate ...

Question 6

Find the displacement of a particle if v(t) = sin t;  .

Accepted Answer

The answer of Find the displacement of a particle if...

Question 7

Find all values of x* in the interval [0,4] that satisfy the Mean-Value Theorem for Integrals, where f(x) = x⁴.

Accepted Answer

The answer of Find all values of x* in the...

Question 8

Evaluate  .

Accepted Answer

The answer of Evaluate  ....

Question 9

A particle moves along with a velocity of v(t) = t⁴ - t⁸ m/s along an s-axis. Find the displacement of the particle during the period 0 $\le$ t $\le$ 3.

Accepted Answer

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

Question 10

Find the distance an object travels if its velocity is v(t) = t - 6t² in m/s, where 0 $\le$ t $\le$ 2.

Accepted Answer

The answer of Find the distance an object travels if...

Question 11

Answer true or false. If a velocity v(t) = t3 on [-5, 5], the displacement is given by  .

Accepted Answer

A) True 
 B)False

Question 12

Simplify e^ln⁹⁺^ln^x .

Accepted Answer

The answer of Simplify e^ln⁹⁺^ln^x ....

Question 13

Find the displacement of a particle if v(t) = cos t;  .

Accepted Answer

A)  -1 
B)  0 
C)  2 
D)   
E)   $\pi$

Question 14

For  , what would be a good choice for u?

Accepted Answer

The answer of For  , what would be a...

Question 15

Find the average value of f(x) = 4x + 5 over [0, 2] and find a point x* in [0,2] such that  .

Accepted Answer

The answer of Find the average value of f(x) =...

Question 16

Answer true or false. For  a good choice for u is 1 - x .

Accepted Answer

A) True 
 B)False

Question 17

Find the displacement of an object if its velocity is v(t) = t⁴- 4t in m/s, where 0 $\le$ t $\le$ 2.

Accepted Answer

The answer of Find the displacement of an object if...

Question 18

Simplify. e³^{ln x} =

Accepted Answer

The answer of Simplify. e³^{ln x} =...

Question 19

Answer true or false.  = 0 .

Accepted Answer

A) True 
 B)False

Question 20

Find the average value of f(x) = e x - 2 over the interval [-1, 1]. Approximate value to three decimal places.

Accepted Answer

A)  -0.825 
B)  -1.650 
C)  2.718 
D)  0.359 
E)  -0.855

Exam 5: Integration

Find the displacement of a particle if v(t) = sin t; [0, $\pi$ ].

Find the displacement of an object if its velocity is v(t) = t⁴ - 2t in m/s, where 0 $\le$ t $\le$ 2.

Find the distance an object travels if its velocity is v(t) = 4t³ - 4t in m/s, where 0 $\le$ t $\le$ 4.

Evaluate .

Evaluate

Find the displacement of a particle if v(t) = sin t; .

Find all values of x* in the interval [0,4] that satisfy the Mean-Value Theorem for Integrals, where f(x) = x⁴.

Evaluate .

A particle moves along with a velocity of v(t) = t⁴ - t⁸ m/s along an s-axis. Find the displacement of the particle during the period 0 $\le$ t $\le$ 3.

Find the distance an object travels if its velocity is v(t) = t - 6t² in m/s, where 0 $\le$ t $\le$ 2.

Answer true or false. If a velocity v(t) = t³ on [-5, 5], the displacement is given by .

Simplify e^ln⁹⁺^ln^x .

Find the displacement of a particle if v(t) = cos t; $Find the displacement of a particle if v(t) = cos t; . A) -1 B) 0 C) 2 D) E) \pi$ .

For , what would be a good choice for u?

Find the average value of f(x) = 4x + 5 over [0, 2] and find a point x* in [0,2] such that .

Answer true or false. For a good choice for u is 1 - x.

Find the displacement of an object if its velocity is v(t) = t⁴- 4t in m/s, where 0 $\le$ t $\le$ 2.

Simplify. e³^{ln x} =

Answer true or false. = 0 .

Find the average value of f(x) = e ^x - 2 over the interval [-1, 1]. Approximate value to three decimal places.

Exam 5: Integration

Find the displacement of a particle if v(t) = sin t; [0, π\piπ ].

Find the displacement of an object if its velocity is v(t) = t4 - 2t in m/s, where 0 ≤\le≤ t ≤\le≤ 2.

Find the distance an object travels if its velocity is v(t) = 4t3 - 4t in m/s, where 0 ≤\le≤ t ≤\le≤ 4.

Evaluate .

Evaluate

Find the displacement of a particle if v(t) = sin t; .

Find all values of x* in the interval [0,4] that satisfy the Mean-Value Theorem for Integrals, where f(x) = x4.

Evaluate .

A particle moves along with a velocity of v(t) = t4 - t8 m/s along an s-axis. Find the displacement of the particle during the period 0 ≤\le≤ t ≤\le≤ 3.

Find the distance an object travels if its velocity is v(t) = t - 6t2 in m/s, where 0 ≤\le≤ t ≤\le≤ 2.

Answer true or false. If a velocity v(t) = t3 on [-5, 5], the displacement is given by .

Simplify eln 9 + ln x .

Find the displacement of a particle if v(t) = cos t; .

For , what would be a good choice for u?

Find the average value of f(x) = 4x + 5 over [0, 2] and find a point x* in [0,2] such that .

Answer true or false. For a good choice for u is 1 - x .

Find the displacement of an object if its velocity is v(t) = t4- 4t in m/s, where 0 ≤\le≤ t ≤\le≤ 2.

Simplify. e3 ln x =

Answer true or false. = 0 .

Find the average value of f(x) = e x - 2 over the interval [-1, 1]. Approximate value to three decimal places.

Find the displacement of a particle if v(t) = sin t; [0, $\pi$ ].

Find the displacement of an object if its velocity is v(t) = t⁴ - 2t in m/s, where 0 $\le$ t $\le$ 2.

Find the distance an object travels if its velocity is v(t) = 4t³ - 4t in m/s, where 0 $\le$ t $\le$ 4.

Find all values of x* in the interval [0,4] that satisfy the Mean-Value Theorem for Integrals, where f(x) = x⁴.

A particle moves along with a velocity of v(t) = t⁴ - t⁸ m/s along an s-axis. Find the displacement of the particle during the period 0 $\le$ t $\le$ 3.

Find the distance an object travels if its velocity is v(t) = t - 6t² in m/s, where 0 $\le$ t $\le$ 2.

Answer true or false. If a velocity v(t) = t³ on [-5, 5], the displacement is given by .

Simplify e^ln⁹⁺^ln^x .

Find the displacement of a particle if v(t) = cos t; $Find the displacement of a particle if v(t) = cos t; . A) -1 B) 0 C) 2 D) E) \pi$ .

Answer true or false. For a good choice for u is 1 - x.

Find the displacement of an object if its velocity is v(t) = t⁴- 4t in m/s, where 0 $\le$ t $\le$ 2.

Simplify. e³^{ln x} =

Find the average value of f(x) = e ^x - 2 over the interval [-1, 1]. Approximate value to three decimal places.