Find the surface area of the torus obtained by rotating the circle x2 + (y – b)? =r² about the x-axis (Figure 20). (0, b+ r) (0, b) FIGURE 20 Torus obtained by rotating a circle about the x-axis.

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A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

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A: We calculate this by using concepts of line Integrals !

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Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

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