007B Sample Midterm 1, Problem 5 Detailed Solution

From Math Wiki
Jump to navigation Jump to search

Find the area bounded by    and    from    to  

Background Information:  
1. You can find the intersection points of two functions, say  

       by setting    and solving for  

2. The area between two functions,    and    is given by  

       for    where    is the upper function and    is the lower function.


Step 1:  
We start by finding the intersection points of these two functions.
So, we consider the equation   
In the interval    the solutions to this equation are
Also, for    we have


Step 2:  
The area bounded by these functions is given by


Then, we integrate to get

Final Answer:  

Return to Sample Exam