# Calculus 2 : Definite Integrals

## Example Questions

### Example Question #81 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

### Example Question #81 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

### Example Question #82 : Definite Integrals

Explanation:

First, integrate the function. Remember, when integrating, raise the exponent by 1 and then put that result on the denominator. The first step should look like this: . Then, evaluate the function at 3 and subtract from the result when you plug in 0. .

### Example Question #81 : Definite Integrals

Explanation:

To integrate, remember to raise the exponent by 1 and then put that result on the denominator: . Then, evaluate at 3 and then 1. Subtract the two results. .

### Example Question #85 : Definite Integrals

Explanation:

First, integrate the expression, remembering to add one to the exponent and then putting that result on the denominator: . Then evaluate at 3 and then 1. Subtract the results: .

### Example Question #86 : Definite Integrals

Evaluate the following definite integral:

Explanation:

### Example Question #87 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

### Example Question #88 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

In this step it should be pointed out that natural log cannot be evaluated for values less than 1 thus there is no solution to this problem.

### Example Question #89 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

Evaluate.