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)....

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.