Calculus 2 : Finding Integrals

Study concepts, example questions & explanations for Calculus 2

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1 3 4 5 6 7 8 9 68 69

Example Question #341 : Integrals

Evaluate:

Possible Answers:

Correct answer:

Explanation:

,

so

Example Question #1 : Finding Integrals

Evaluate:

Possible Answers:

The integral is undefined.

Correct answer:

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:

Possible Answers:

The integral is undefined.

Correct answer:

Explanation:

Example Question #1 : Finding Integrals

Evaluate: 

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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 #2 : Finding Integrals

 

Evaluate:

Possible Answers:

 

 

Correct answer:

 

Explanation:

We evaluate 

The original double integral is now

Example Question #2 : Finding Integrals

 

Evaluate:

Possible Answers:

Correct answer:

Explanation:

We evaluate 

The original double integral is now

Example Question #9 : Finding Integrals

Evaluate:

Possible Answers:

Correct answer:

Explanation:

We evaluate 

The original double integral is now

Example Question #1 : Finding Integrals

Evaluate:

Possible Answers:

Correct answer:

Explanation:

The problem is easier if it is written as follows:

We evaluate 

The original double integral is now

which, similarly to , is equal to 1.

← Previous 1 3 4 5 6 7 8 9 68 69
Learning Tools by Varsity Tutors