Consider the double integral xdA where R = {(x,y) R(x-4) y 4}. (a)...

 

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Consider the double integral xdA where R = {(x,y) € R²(x-4)² ≤ y ≤ 4}. (a) Make a neat, labelled sketch of the region R in the ry-plane. (b) Express this double integral as an integral with respect to y first, then z a dy dr rather than a dA, with correct limits of integration. that is using (c) Express this double integral as an integral with respect to a first, then y that is using a dx dy rather than a dA, with correct limits of integration (reversing the order of integration compared to (b) above). (d) Evaluate this double integral using either your answer to (b) or (c). Consider the double integral xdA where R = {(x,y) € R²(x-4)² ≤ y ≤ 4}. (a) Make a neat, labelled sketch of the region R in the ry-plane. (b) Express this double integral as an integral with respect to y first, then z a dy dr rather than a dA, with correct limits of integration. that is using (c) Express this double integral as an integral with respect to a first, then y that is using a dx dy rather than a dA, with correct limits of integration (reversing the order of integration compared to (b) above). (d) Evaluate this double integral using either your answer to (b) or (c).

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b Express the double integral as an integral with respect to y first then z The region ... View the full answer