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LAB Integration Surface Color Previously, ue learned how to interpret the integral ofy =ftx) over a given domain ofvalues_ Today, we explorv how to interpret the integral of z over a green domain of values O_ Review a. For a ftnction y = nx), we can approximate the area under it using what shapes? b. Using this method, we div1cLe the domain into what shapes? c. For y = x3, approximate the area bet-ween the graph and the x-axis for 1 x 3 using 4 intavals (use any method e.g. let right sum, etc_)_ Write down an integral for the exact area 1 _ For a. We can approximate the volume under it using what shapes? b. Usmg this method, we divide the domain into what shapes? 2. Your have contour maps for 6 different pieces of cake with a 2"x4" base. Let your z-values represent the height (m inches) of the cake. Pick one piece of cake and estimate the volume of the cake Describe nur method- what each number represents, and your method for setting up your calculation 3. How could you get a better estimate of the volume? Be specific. 4 _ Write down the expression which finds the volume exactly 5 _ Challenge: Can we use this approximation method if the domain is not a rectangle? Ifyes, how? Ifnot, why not? A) What did you learn during this lab? Which activities nu leam it? B) Is there anything you still find conmsing?