Answer to Question #151183 in Calculus for Zeeshan

Question #151183
∫ 2y dx + 3x dy
where d is describe by 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1
1
Expert's answer
2020-12-15T19:41:11-0500

Solution:


1) We need to verify that "\\intop_c(2y)dx\\;+\\;(3x)dy=" "\\iint_D( \\dfrac{\u2202}{\u2202x}(3x)-\\dfrac{\u2202}{\u2202y}(2y)\t)dA" , where D denotes the region bounded by C.


x = cost

y = sin t


"\\int_C2ydx+3xdy=\\int^{ \\tfrac{\\pi}{2}\t}_0[2sint(-sint)+3cost\\;cost]dt=\\dfrac{\\pi}{4}"


"\\iint_D( \\dfrac{\u2202}{\u2202x}(3x)-\\dfrac{\u2202}{\u2202y}(2y)\t)dA=\\iint_DdA=\\dfrac{\\pi}{4}"



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