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# Double Integals, Polar Coordinates and Surface Integrals

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A) Make use of the polar coordinates to evaluate &#8747;&#8747;R&#8730;x2 + y2 dR; where R is the region bounded by the semicircle y = &#8730;2x - x2 and the line y = x.

b) Evaluate the surface integral &#8747;&#8747;S x2 dS, where S is the upper half of the
sphere x2 + y2 + z2 = 4.

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Qn 5.
a) Make use of the polar coordinates to evaluate ∫∫R√x2 + y2 dR; where R is the region bounded by the semicircle y = √2x - x2 and the line y = x.

The region is the labelled by the red curves.
First find the intersection of the semicircle ...

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