Question 1

Evaluate the given definite integral.

Accepted Answer

The answer of Evaluate the given definite integral. ...

Question 2

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 3

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 4

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 5

Find the area of the region under the graph of the function f on the interval [a, b].

Accepted Answer

The answer of Find the area of the region under...

Question 6

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. ...

Question 7

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 8

Find the area of the region under the graph of the function  on the interval  .

Accepted Answer

The answer of Find the area of the region under...

Question 9

Find the area of the region under the graph of the function  on the interval  , using the fundamental theorem of calculus. Then verify your result using geometry.

Accepted Answer

The answer of Find the area of the region under...

Question 10

Find the area of the region under the graph of the function  on the interval  .

Accepted Answer

The answer of Find the area of the region under...

Question 11

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 12

Find the area of the region under the graph of the function  on the interval  , using the fundamental theorem of calculus. Then verify your result using geometry.

Accepted Answer

The answer of Find the area of the region under...

Question 13

Find the area of the region under the graph of the function  on the interval  .

Accepted Answer

To find the area under the curve, we need to integrate the function with respect to x from 0 to 1:

∫₀¹ 11e^(−8x−3) dx

We can use integration by substitution, where u = −8x − 3, du/dx = −8, and dx = −(1/8) du:

∫₋₃⁻⁰ 11e^u (−1/8) du

= (−11/8) ∫₋₃⁻⁰ e^u du

= (−11/8) [e^u]₋₃⁻⁰

= (−11/8) (e⁰ − e^₋₃)

= (11/8) (e^₋₃ − 1)

The correct answer is hence (C).

Question 14

Find the average value of the function  over the indicated interval  .

Accepted Answer

The answer of Find the average value of the function...

Question 15

Find the average value of the function  over the interval  .

Accepted Answer

The answer of Find the average value of the function...

Question 16

Evaluate the definite integral.

Accepted Answer

Without any limits of integration provided, we cannot compute a definite integral. The answer choices all have the same expression for the integrand, just with different unique identifiers tacked onto the end. Therefore, the correct answer choice can be determined by a process of elimination:

- A and B have the same identifier up to the third block, but the fourth block is different. We can eliminate them.
- D has a different fourth block from C. However, we have no way of knowing which of these two answer choices is correct, since we have no limits of integration. Therefore we cannot completely eliminate D. 
- C has a different fourth block from A and B, but the same fourth block as D. Therefore, the only reasonable choice we can make here is to select C.

Question 17

A bottle of white wine at room temperature (  ) is placed in a refrigerator at 4 P.M. Its temperature after t hours is changing at the rate of   . By how many degrees will the temperature of the wine have dropped by 8 P.M.? Please round your answer to one decimal place.
__________  What will the temperature of the wine be at 8 P.M.? Please round your answer to one decimal place.
__________

Accepted Answer

The answer of A bottle of white wine at room...

Question 18

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 19

Find the area of the region under the graph of the function  on the interval  .

Accepted Answer

The answer of Find the area of the region under...

Question 20

Find the area of the region under the graph of the function  on the interval  , using the fundamental theorem of calculus. Then verify your result using geometry.

Accepted Answer

The answer of Find the area of the region under...

Quiz 6: Integration

Evaluate the given definite integral.

Evaluate the definite integral.

Evaluate the definite integral.

Evaluate the definite integral.

Find the area of the region under the graph of the function f on the interval [a, b].

Evaluate the definite integral.

Evaluate the definite integral.

Find the area of the region under the graph of the function on the interval .

Find the area of the region under the graph of the function on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.

Find the area of the region under the graph of the function on the interval .

Evaluate the definite integral.

Find the area of the region under the graph of the function on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.

Find the area of the region under the graph of the function on the interval .

Find the average value of the function over the indicated interval .

Find the average value of the function over the interval .

Evaluate the definite integral.

Evaluate the definite integral.

Find the area of the region under the graph of the function on the interval .

Find the area of the region under the graph of the function on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.