### All Calculus 2 Resources

## Example Questions

### Example Question #2 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Evaluate :

**Possible Answers:**

**Correct answer:**

By the Fundamental Theorem of Calculus, we have that . Thus, .

### Example Question #3 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Evaluate when .

**Possible Answers:**

**Correct answer:**

Via the Fundamental Theorem of Calculus, we know that, given a function, .

Therefore .

### Example Question #4 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Evaluate when .

**Possible Answers:**

**Correct answer:**

Via the Fundamental Theorem of Calculus, we know that, given a function , . Therefore, .

### Example Question #1 : Fundamental Theorem Of Calculus

Evaluate when .

**Possible Answers:**

**Correct answer:**

Via the Fundamental Theorem of Calculus, we know that, given a function , . Therefore, .

### Example Question #5 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Suppose we have the function

What is the derivative, ?

**Possible Answers:**

**Correct answer:**

We can view the function as a function of , as so

where .

We can find the derivative of using the chain rule:

where can be found using the fundamental theorem of calculus:

So we get

### Example Question #2 : Fundamental Theorem Of Calculus

If , what is ?

**Possible Answers:**

**Correct answer:**

By the Fundamental Theorem of Calculus, we know that given a function, .

Thus,

### Example Question #3 : Fundamental Theorem Of Calculus

If , what is ?

**Possible Answers:**

**Correct answer:**

By the Fundamental Theorem of Calculus, we know that given a function, .

Thus,

### Example Question #4 : Fundamental Theorem Of Calculus

If , what is ?

**Possible Answers:**

**Correct answer:**

By the Fundamental Theorem of Calculus, we know that given a function, .

Thus,

### Example Question #6 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Given

, what is ?

**Possible Answers:**

None of the above.

**Correct answer:**

By the Fundamental Theorem of Calculus, for all functions that are continuously defined on the interval with in and for all functions defined by by , we know that .

Thus, for

,

.

Therefore,

### Example Question #7 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Given

, what is ?

**Possible Answers:**

None of the above.

**Correct answer:**

By the Fundamental Theorem of Calculus, for all functions that are continuously defined on the interval with in and for all functions defined by by , we know that .

Given

, then

.

Therefore,

.