Question

Are people stupid? Why must I do a "double integral" on this problem instead of 2 single ones?

Answer 1

What I'm trying to find is the area bounded between the curves y=1/x and y=sqrtx inside the domain 1<x<3.

The book is telling me to use a double integral, but can't I just take the integral from x=1 to x=3 of y=sqrtx and subtract the integral from x=1 to x=3 of y=1/x to get the area? Doesn't make sense!

Answer 2

\[ \iint_S dA = A\]

Answer 3

you like the integral sign much? :P

Answer 4

if you do manipulate it carefully, this changes into single integral. of course you can do it via single integral directly.

Answer 5

as experiment pointed out, a single integral is just a dumbed down version of a double integral:
\[\int_{a}^{b}\int_{g(x)}^{f(x)}~~dy~dx\]
\[\int_{a}^{b}~f(x)-g(x)~dx\]

Answer 6

The more math you studied, the more variations of notation we encounter.