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Question 02 (b) 

Consider a solid whose base in the xyplane is the finite region bounded by the curves y = x^{2} and y = 2 − x^{2}. The cross sections of the solid perpendicular to the xaxis with one side in the xyplane are squares. Find the volume of this solid. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Draw a picture. What are the limiting values on the xaxis? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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If we follow the hint, we can draw a diagram similar to the one pictured on the right . We have drawn the axis so that we see the xy plane in its familiar 2D position.
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Volume (cross section) 