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Unformatted text preview: x . Taking F = (6 xy 5 ) i + (1 + x 2 y-y 6 ) j , a) set up an integral in x alone that represents the ux of F over C . (Give integrand and limits, but do not evaluate); b) calculate the ux of F over C by using Greens Theorem in the normal form. (Note that C is not closed). Problem 5. Show that the value of I C ( y 2-2 y ) dx + 2 xy dy around a positively oriented circle C depends only on the size of the circle, and not on its position. Problem 6. Consider the integral Z Z R ( x + y ) 4 (3 x-y ) 4 dxdy , where R is the triangle with vertices at x =-1 and x = 3 on the x-axis, and y = 3 on the y-axis. Let u = x + y and v = 3 x-y . Express the double integral in uv-coordinates; use as the order of integration dv du . Problem 7. Calculate the volume in the upper half plane contained between the cone, z = ( x 2 + y 2 ) 1 / 2 and the sphere x 2 + y 2 + z 2 = 2....
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This note was uploaded on 05/14/2010 for the course 18.02A 18.02A taught by Professor Johnbush during the Winter '10 term at MIT.
- Winter '10