Question

Ketch the bounded region enclosed by y=e2x,y=e4xy=e2x,y=e4x and x=1x=1. decide whether to integrate with respect to xx or yy, and then find the area of the region.

Answer 1

A) See the attached graph. The purple area appears to be what you want to find.

b) Integrating with respect to x seems much easier. If one were to integrate over y, there would need to be two regions of integration: [1, e^2] and [e^2, e^4].

c) $\int\limits^1_0 {(e^{4x}-e^{2x})} \, dx =\frac{1}{4}(e^{4}-1) -\frac{1}{2}(e^{2}-1) \approx 10.2050094588$