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Unformatted text preview: 5.(6+6+6 pts.) For each of the vector &elds below, check whether it is conservative or not. Find a potential function if it is conservative. (a) F ( x; y; z ) = h x 3 ; y 3 ; z 3 + 1 i . (b) F ( x; y; z ) = h e x cos( y ) ; tan ( y ) e x cos( y ) (sec ( y ) & x ) ; xy i . (c) F ( x; y ) = h (1 + xy ) e xy ; e y + x 2 e xy i . 6.(6+12 pts.) (a) Show that I C (2 xy + e x 2 ) dx + (( x + 1) 2 + ln(2 + sin ( y ))) dy = 2 I C ( x & y ) dy where C is the plane curve parametrized as x = cos ( t ) + 1 10 cos 2 ( t ) , x = sin ( t ) + 1 10 cos 2 ( t ) for ± t ± 2 & . (Hint: Use Green&s theorem.) (b) Evaluate the second line integral above directly using the parametrization. (c) What is the area of the region enclosed by C ?...
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- Spring '11
- various
- Calculus, 6 pts, 10 pts, dx dy, dy dx dz, METU Northern Cyprus Campus
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