### All AP Calculus AB Resources

## Example Questions

### Example Question #26 : Techniques Of Antidifferentiation

Integrate:

**Possible Answers:**

**Correct answer:**

The integral of the function is equal to

The rules used for integration were

,

For the definite component of the integration, we plug in the upper limit of integration, and subtract the result of plugging in the lower limit of integration:

### Example Question #27 : Techniques Of Antidifferentiation

Evaluate the integral

**Possible Answers:**

**Correct answer:**

To find the derivative of the expression, we use the following rule

Applying to the integrand from the problem statement, we get

### Example Question #28 : Techniques Of Antidifferentiation

Find the antiderivative of the following.

**Possible Answers:**

**Correct answer:**

Follow the following formula to find the antiderivatives of exponential functions:

Thus, the antiderivative of is .

### Example Question #29 : Techniques Of Antidifferentiation

Find the antiderivative of the following.

**Possible Answers:**

**Correct answer:**

is the derivative of . Thus, the antiderivative of is .

### Example Question #30 : Techniques Of Antidifferentiation

Find the antiderivative of the following.

**Possible Answers:**

**Correct answer:**

is the derivative of . Thus, the antiderivative of is .

### Example Question #31 : Techniques Of Antidifferentiation

Define

Evaluate .

**Possible Answers:**

**Correct answer:**

has different definitions on and , so the integral must be rewritten as the sum of two separate integrals:

Calculate the integrals separately, then add:

### Example Question #21 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Evaluate the integral

**Possible Answers:**

**Correct answer:**

To evaluate the integral, we use the rules for integration which tell us

Applying to the integral from the problem statement, we get

### Example Question #33 : Techniques Of Antidifferentiation

Integrate:

**Possible Answers:**

**Correct answer:**

To evaluate the integral, we can split it into two integrals:

After integrating, we get

where a single constant of integration comes from the sum of the two integration constants from the two individual integrals, added together.

The rules used to integrate are

,

### Example Question #34 : Techniques Of Antidifferentiation

Solve:

**Possible Answers:**

**Correct answer:**

The integral is equal to

and was found using the following rule:

where

### Example Question #35 : Techniques Of Antidifferentiation

Solve:

**Possible Answers:**

**Correct answer:**

To integrate, we can split the integral into the sum of two separate integrals:

Integrating, we get

which was found using the following rules:

,

Note that the constants of integration were combined to make a single integration constant in the final answer.

(The first integral can be rewritten as for clarity.)

Certified Tutor

Certified Tutor