GRE Subject Test: Math : Integration by Parts

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Integration By Parts

Integrate the following.

Possible Answers:

Correct answer:

Explanation:

Integration by parts follows the formula: 

So, our substitutions will be  and 

which means  and 

Plugging our substitutions into the formula gives us:

           

Since  , we have:

 

, or

Example Question #2 : Integration By Parts

Evaluate the following integral. 

Possible Answers:

Correct answer:

Explanation:

Integration by parts follows the formula:

                              

In this problem we have  so we'll assign our substitutions:

 and 

which means  and 

Including our substitutions into the formula gives us: 

                      

     We can pull out the fraction from the integral in the second part:

Completing the integration gives us:

              

              

Example Question #3 : Integration By Parts

Evaluate the following integral. 

Possible Answers:

Correct answer:

Explanation:

Integration by parts follows the formula: 

                

Our substitutions will be  and  

which means  and .

Plugging our substitutions into the formula gives us: 

              

Look at the integral: we can pull out the  and simplify the remaining  as 

.

We now solve the integral:  , so:

 

Example Question #4 : Integration By Parts

Evaluate the following integral.

Possible Answers:

Correct answer:

Explanation:

Integration by parts follows the formula: 

               .

Our substitutions are  and  

which means  and .

Plugging in our substitutions into the formula gives us

We can pull   outside of the integral.

 

Since , we have

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