# HW 11 - Math E-21a Fall 2009 HW #11 problems Problems due...

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1 Math E-21a – Fall 2009 – HW #11 problems Problems due Thurs, Nov 19 : Section 12.9 : (these were inadvertently omitted from last week’s PDF of the assignment) 12. Evaluate the integral (4 8 ) R x ydA  , where R is the parallelogram with vertices (1 ,3 ) , (1, 3) , (3, 1) , and (1, 5). Use the coordinate transformation 11 44 { ( ), ( 3 )} x uvy v u  . 13. Evaluate the integral 2 R x dA , bounded by the ellipse 22 94 3 6 xy . Use the coordinate transformation {2 , 3 } x uy v  . [ Note : In both of these exercises, though the transformation is provided, you should be able to come up with the appropriate coordinate transformation by considering the geometry of the region involved.] Section 13.1 : 6. Sketch the vector field (, ) y x x y i j F . 25. Find the gradient vector field f of ( , ) 2 f xy x y x and sketch it. There's a good java-based tool for showing vector fields and flows in R 2 Choose the PPLANE option. You can enter new x and y component functions for the vector field or change the size of the window. To see a trajectory (flow), just click on a point in the phase-plane. Section 13.2 : In problems 2, 5, and 8, evaluate the line integral, where C is the given curve.

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## HW 11 - Math E-21a Fall 2009 HW #11 problems Problems due...

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