MATH 31A Midterm: Math 31A Exam 20
Document Summary
This test is closed book and closed notes. For full credit show all of your work (legibly!). Each problem is worth 10 points: find the area between the curves y = |1 x2| and y = 7 x2. Since we are dealing with an absolute value, it is better to break it up so that we can drop the absolute value. |1 x2| = x2 1. 1 x2 x2 1 if x 1; if 1 x 1; if 1 x. So when we integrate we will similarly break our integral into pieces and integrate each corresponding piece. It is also easy to see that the two points of intersection for this curve occur when x2 1 = 7 x2 or x2 = 4 or x = 2. So to nd the area we will integrate from 2 to 2 and since in that range we have 7 x2 |1 x2| then we know 7 x2 will be on top.
