(a) Write but do not evaluate, an expression involving an integral that gives the perimeter of R in terms of k. b) The Region R rotated about the x-axis to form a solid . Find the Volume terms of k.

1. Let f(x) = e2x. Let R be the region in the first quadrant bounded by the graph of f, the oordinate axes, and the vertical line x = k, where k > 0. The region R is shown in figure below. ( k , e 2 k ) R k