Let S be the surface bounded by the portions of the unit sphere x2+y2+z2 = 1,the x–y, y–z, and x–z planes with positive coordinates (this is just the surface of one- eighth of the solid sphere). Evaluate the double integral of F · dS S where F(x, y, z) = e^(y+z) tan(−y)i + 2yj + ln(x) sin(y)e^(x^2) k. Hint: Use the Divergence Theorem.


  1. Let S be the surface bounded by the portions of the unit sphere x2+y2+z2 = 1,the x–y, y–z, and x–z planes with positive coordinates (this is just the surface of one-

    eighth of the solid sphere). Evaluate the double integral of

    F · dS S

    where F(x, y, z) = e^(y+z) tan(−y)i + 2yj + ln(x) sin(y)e^(x^2) k. Hint: Use the Divergence Theorem.

Let S be the surface bounded by the portions of the unit sphere x2+y2+z2 = 1,the x–y, y–z, and x–z planes with positive coordinates (this is just the surface of one- eighth of the solid sphere). Evaluate the double integral of F · dS S where F(x, y, z) = e^(y+z) tan(−y)i + 2yj + ln(x) sin(y)e^(x^2) k. Hint: Use the Divergence Theorem.


  1. Let S be the surface bounded by the portions of the unit sphere x2+y2+z2 = 1,the x–y, y–z, and x–z planes with positive coordinates (this is just the surface of one-

    eighth of the solid sphere). Evaluate the double integral of

    F · dS S

    where F(x, y, z) = e^(y+z) tan(−y)i + 2yj + ln(x) sin(y)e^(x^2) k. Hint: Use the Divergence Theorem.

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