Question: Consider the one-forms 1 and 2 on R3 given by 1 =(ey +cos(x+z)) dx+(z+y) dy+y dz and 2 =xey dy+(z2ez cos(x+z)) dz. Let S R3

Consider the one-forms 1 and 2 on R3 given by 1 =(ey +cos(x+z)) dx+(z+y) dy+y dz and 2 =xey dy+(z2ez cos(x+z)) dz. Let S R3 be an oriented surface, with S its oriented boundary. Use Stokes' theorem to show that d1 = 2. S S

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