x [0,2]? What is the solution for the area under the curve if the interval is: x

Question

x [0,2]? What is the solution for the area under the curve if the interval is: x [1,3]? This graph consist of segment and semicircle, as shown in the figure below .Evaluate the following definite integrals. Again please attach a Maple file (this may be combined with the file for problem one Define the function over the four intervals, which will allow you to find the area under the curve from x [-4,6] In order to do this, you will need to review the techniques of finding the equations of lines and circles, given the data from the image. Show all of your steps. Integrate over each integral so that you arrive at: Integrate over each integral so that you arrive at: I want to see the solution as a decimal (hint: you may have to use the f solve command, rather than just plain solve). Does your answer make sense, given the four separate integrals? What other comments do you have about this problem?

Explanation / Answer

a)for [-4,-2], y+1 = 0.5(x+4) => y = 0.5x + 1 for[-2,2], x^2+y^2 = 4 for[2,4], y-2 = x-4 => y = x-2 for[4,6], y-2 = -1(x-4) =>y = -x+6 b)Area under the curve = (0.5*2*1) + ((11/7)*2^2) + (0.5*2*2) + (0.5*2*2) = 11.2857

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