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The Region D In R2\mathbb { R } ^ { 2 }

question 79

Essay

The region D in R2\mathbb { R } ^ { 2 } shown below is bounded by x = 1, y=exy = e ^ { x } , and y=1x2y = 1 - x ^ { 2 } .  The region D in  \mathbb { R } ^ { 2 }  shown below is bounded by x = 1,  y = e ^ { x }  , and  y = 1 - x ^ { 2 }  .   (a) Compute  \iint _ { R } x d A  by finding  \int _ { 0 } ^ { 1 } \int _ { 1 - x ^ { 2 } } ^ { e ^ { x } } x d y d x  .(b) Write down the integral or integrals needed to compute  \iint _ { R } x d A  with the order of integration reversed. (a) Compute RxdA\iint _ { R } x d A by finding 011x2exxdydx\int _ { 0 } ^ { 1 } \int _ { 1 - x ^ { 2 } } ^ { e ^ { x } } x d y d x .(b) Write down the integral or integrals needed to compute RxdA\iint _ { R } x d A with the order of integration reversed.

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