Hello, can someone please help me with this one... Find a nonzero function h for which F(x,y) = h(x)[xsin y + y cos y]i + h(x)[x cos y - y sin y]j is conservative. Thanks!
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The condition you need to satisfy is df/dy = dg/dx (these are actually partial derivatives df/dy = h(x){xcos(y) -ysin(y)} +h(x)cos(y) dg/dx = h ' (x){xcos(y) -ysin(y)} + h(x)cos(y) Setting the two equal we obtain h ' (x) = h(x) or h(x) = e^x
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