### All Calculus 2 Resources

## Example Questions

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

,

so

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

The integral is undefined.

**Correct answer:**

Rewrite this as follows:

Substitute . Then and , and the bounds of integration become 2 and 3, making the integral equal to

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

The integral is undefined.

**Correct answer:**

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

Substitute ; so and , and the bounds of integration become 2 and ; the above becomes

### Example Question #5 : Finding Integrals

Which of the following functions makes the statement true?

**Possible Answers:**

**Correct answer:**

Therefore, we are looking for a value of for which

, or, equivalently,

, or

The only choice that makes an element of this set is

.

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

An easy way to look at this is to note that on the interval , the integrand

can be rewritten as

Therefore,

The antiderivative of is . We can evaluate at each boundary of integration:

Then

The original integral can be evaluated as

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

We evaluate

The original double integral is now

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

We evaluate

The original double integral is now

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

We evaluate

The original double integral is now

### Example Question #1 : Finding Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

The problem is easier if it is written as follows:

We evaluate

The original double integral is now

which, similarly to , is equal to 1.