In the case of two functions each with an antiderivative (indefinite integral) that increases forever without bound toward $+∞$ as $x$ approaches $+∞$ andor $-∞$, the area under each curve is infinite, i.e. some degree/magnitude/measure of $|∞|$. However, clearly they are not all equivalent. The negative_1st derivative with more modest end-behavior slopes intuitively and visually are smaller in scale than ones with more rapid end-behavior growth.
Would the ratio of one area under an integrable curve to another area under a different integrable curve simply be the former indefinite integral divided by the latter indefinite integral? Does this hold for non-infinite areas of integral curves as well, over finite and infinite domains? If so, then logically this should extend to less-finite integrals.