MPI_Ex4_ans - PHYS1315 Methods in Physics I 2012/13...

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PHYS1315 Methods in Physics I2012/13 Solutions to Exercise 41. (a)Z31Z102xyx2+ 1dxdy=Z31y[ln(x2+ 1)]10dy=Z31yln 2dy=12y2ln 231= 4 ln 2
Zπ/30Zπ/20
Zπ/30ycosx+12x2sinyπ/20
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Z3/20Z9-4y2-9-4y2y dxdy=Z3-3Z129-x20y dydx=Z3-318(9-x2)dx=98x-124x33-3=92(c) The region of integration is shown in the figure below.Z20Z1y/2cosx2dxdy=Z10Z2x0cosx2dydx=Z102xcosx2dx=sinx210= sin 1
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