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

Essay

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.