Calculus 2 : Definite Integrals

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #81 : Definite Integrals

Evaluate.

Possible Answers:

Answer not listed.

Correct answer:

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.

Possible Answers:

Answer not listed.

Correct answer:

Explanation:

In this case, .

The antiderivative is  .

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

Example Question #82 : Definite Integrals

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

Explanation:

Example Question #87 : Definite Integrals

Evaluate.

Possible Answers:

Answer not listed.

Correct answer:

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.

Possible Answers:

Answer not listed

Correct answer:

Answer not listed

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.

Possible Answers:

Answer not listed.

Correct answer:

Explanation:

In this case, .

The antiderivative is  .

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

Example Question #83 : Definite Integrals

Evaluate.

Possible Answers:

Answer not listed.

Correct answer:

Explanation:

In this case, .

The antiderivative is  .

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

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