Chapter 16.6, Problem 5PT

Write an iterated integral for the area of that part of the plane z = x that is above the region D at the right.

1. a) ${\displaystyle {\int }_0^1{\displaystyle {\int }_x^{x^2}\sqrt{x^2+1}dydx}}$
2. b) ${\displaystyle {\int }_0^1{\displaystyle {\int }_{x^2}^x\sqrt{x^2+1}dydx}}$
3. c) ${\displaystyle {\int }_0^1{\displaystyle {\int }_{x^2}^x\sqrt{2}dydx}}$
4. d) ${\displaystyle {\int }_0^1{\displaystyle {\int }_y^{\sqrt{y}}\sqrt{y+1}dxdy}}$