# High School Math : Integrals

## Example Questions

### Example Question #18 : Finding Indefinite Integrals

What is the indefinite integral of ?

Explanation:

To find the indefinite integral, we use the reverse power rule. That means we raise the exponent on the variables by one and then divide by the new exponent.

Remember to include a  when doing integrals. This is a placeholder for any constant that might be in the new expression.

### Example Question #71 : Comparing Relative Magnitudes Of Functions And Their Rates Of Change

What is the indefinite integral of ?

Explanation:

To find the indefinite integral, we can use the reverse power rule. Raise the exponent of the variable by one and then divide by that new exponent.

We're going to treat  as .

Remember to include the  when taking the integral to compensate for any constant.

Simplify.

### Example Question #20 : Finding Indefinite Integrals

What is the indefinite integral of ?

Explanation:

To find the indefinite integral, we can use the reverse power rule. We raise the exponent of the variable by one and divide by our new exponent.

Remember to include a  to cover any potential constant that might be in our new equation.

### Example Question #21 : Finding Indefinite Integrals

What is the indefinite integral of ?

Explanation:

Just like with the derivatives, the indefinite integrals or anti-derivatives of trig functions must be memorized.

### Example Question #22 : Finding Indefinite Integrals

Explanation:

To find the indefinite integral of our given equation, we can use the reverse power rule: we raise the exponent by one and then divide by that new exponent.

Don't forget to include a to compensate for any constant!

### Example Question #23 : Finding Indefinite Integrals

What is the indefinite integral of  with respect to ?

Explanation:

To find the indefinite integral, we're going to use the reverse power rule: raise the exponent of the variable by one and then divide by that new exponent.

Be sure to include  to compensate for any constant!

### Example Question #24 : Finding Indefinite Integrals

Explanation:

To find the indefinite integral, or anti-derivative, we can use the reverse power rule. We raise the exponent of each variable by one and divide by that new exponent.

Don't forget to include a  to cover any constant!

Simplify.

### Example Question #25 : Finding Indefinite Integrals

Explanation:

To find the indefinite integral of , we can use the reverse power rule. To do this, we raise our exponent by one and then divide the variable by that new exponent.

Don't forget to include a  to cover any constant!

### Example Question #61 : Asymptotic And Unbounded Behavior

Determine the indefinite integral:

Explanation:

, so this can be rewritten as

Set . Then

and

Substitute:

The outer factor can be absorbed into the constant, and we can substitute back:

### Example Question #62 : Asymptotic And Unbounded Behavior

Evaluate:

Explanation:

Set . Then

and

Also, since , the limits of integration change to  and .

Substitute: