Exercises for Chapter 15, Question 15.151) Write the iterated integral o Si, S. f(x, y, z) dz dy dx as an integral over a region in R*and then rewrite it in a different order of integration.

∫ (e3x+5ex+2  divided by  ex) dx a.) Compute the integral

12. Evaluate the integral: xe dx A. c. 12e** + C В. 12 +C D. +C

Consider switching an integral in the first quadrant x > 0, y> 0 from Cartesian coordinates x, y to hyperbolic coordinates u, v which are related as u = ln V = The area element transforms as dædy |detJ\dudv. Find the Jacobian det J| as expressed in the coordinates u,v.