Mathematics: Let r be the region in the plane bounded by y=x^2, y=0, and x=1. set up an iterated double integral to evaluate double integral of e^(y/x)

Let r be the region in the plane bounded by y=x^2,

Ответ:

glitterpanda2468

17.01.2022

One way to set up the integral is to write it as

$\displaystyle\iint_Re^{y/x}\,\mathrm dA=\int_{x=0}^{x=1}\int_{y=0}^{y=x^2}e^{y/x}\,\mathrm dy\,\mathrm dx$

In the opposite order, you could use the equivalent

$\displaystyle\iint_Re^{y/x}\,\mathrm dA=\int_{y=0}^{y=1}\int_{x=\sqrt y}^{x=1}e^{y/x}\,\mathrm dx\,\mathrm dy$

It's not clear whether you actually have to evaluate the integral or not; I suspect no, since either integrand taken with respect to

does not have an elementary antiderivative.