Double integrals

It's not clear why you're trying to set up a double integral. From the information provided, you should be able to calculate the area between the curves using the difference of two single integrals.

The question asks me to solve using a double integral.

Let $f(x)$ and $g(x)$ be curves that intersect at $x=0$ and $x=1$.

Then the area between them is $\left| \int_{0}^{1}f(x)dx-\int_{0}^{1}g(x)dx \right| =\left| \int_{0}^{1}f(x)-g(x)dx\right|$

It's not clear to me why you would use this method. Could you share the question in full?

Cryptokyo's method is correct (though you must be careful if the curves cross between 0 and 1). It is single integration.

There is no need to do double integration here. Just calculate int x^2 - int x^3, each from 0 to 1.

Double integrals are used for functions of two variables.

I need to know how to do it since we are studying multiple integration! I need to get the foundations down, like knowing what limits to use on the inside integral are. Do you know how to do it?

The question you have quoted doesn't seem to ask you to use double integration, so I'm not sure why you insist you're supposed to use it.

I mean, you can (trivially) rewrite a standard integral as a double one, but it's just obfuscation - I can't see an actual reason to do it here.

'Use a double integral' it says. It's no good finding the area between two curves using standard integration in an exam if it asks for a double integral. I also thought when we had our first lesson on this last week 'what's the point using double integration for a simple right angled triangle', but that was beside the point.

It's not as if you have to be in the deep end to start using it.

If you guys thinks it's that trivial - you don't have to help. I'll try to find it out or ask my teacher next time we meet.