# Calculus 2 : Finding Integrals

## Example Questions

Evaluate:

Explanation:

,

so

### Example Question #351 : Integrals

Evaluate:

The integral is undefined.

Explanation:

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:

The integral is undefined.

Explanation:

### Example Question #1 : Finding Integrals

Evaluate:

Explanation:

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

### Example Question #1 : Finding Integrals

Which of the following functions makes the statement  true?

Explanation:

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:

Explanation:

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:

Explanation:

We evaluate

The original double integral is now

### Example Question #351 : Integrals

Evaluate:

Explanation:

We evaluate

The original double integral is now

### Example Question #1 : Finding Integrals

Evaluate:

Explanation:

We evaluate

The original double integral is now

Evaluate: