Question

Which integral gives the area of the region in the first quadrant bounded by the axes, y = e^x, x = e^y, and the line x = 4?

The answer is an integral.

I know y=e^x has no area bounded, but I don't know how to incorporate it all.

Answer 1

What's the problem? A straightforward integration. The only wrinkle arises because the boundary changes at x=1. The area is

∫[0,1] e^x dx + ∫[1,4] e^x - ln(x) dx

Answer 2

OH I completely forgot to do the "+". I kept typing in the answer without the "+" and kept getting it wrong and decided to get help on the last try. Thank you very much Steve.

Answer 3

good. I guess we could also have written it as

∫[0,4] e^x - ∫[1,4] ln(x) dx