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The following figure shows four regions bounded by the graph of y=xsinx: R1-R4, whose areas are 1, pi-1, pi+1, and 2pi-1. Use this information to evaluate the following integrals.

Question

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The following figure shows four regions bounded by the graph of y=xsinx: R1-R4, whose areas are 1, pi-1, pi+1, and 2pi-1. Use this information to evaluate the following integrals.

anonymous · Answer

attached is an image of the graph and the problem (35)

anonymous · Answer

I'm unsure of the question. Am I just suppose to obtain the value of the integral by just looking at the graph or do i have to evaluate the actual integral? My book says the answer should be pi. The only way i can see why is because the area of the region between 0 and pi, by looking at the graph, is pi.

anonymous · Answer

Using the same reasoning as above to solve question 38, should i have to take the area from region 2 minus the area from regions 3 and 4 to obtain this answer?
$$\pi-1-(\pi+1+2\pi-1)=-1$$