TITLE: Finding the limits for a double integral
QUESTION [0 upvotes]: Question: Find the area enclosed by the two curves $y = x^2$ and $y = x^4$ using a double integral.
My attempt: I believe the limits would be $A$ = {$(x,y): -1 \lt x \lt 1,  x^4 \lt y \lt x^2$} 
This is because the graph y=x^4 is smaller during the interval $-1 \lt x \lt 1$. Is this correct?

REPLY [0 votes]: Yes, it's correct, and note that:
$$
\int_{-1}^1\int_{x^4}^{x^2}dydx=\int_{-1}^1(x^2-x^4)dx=\int_{-1}^1x^2 dx-\int_{-1}^1x^4dx
$$
where the last integral is the difference of the areas under the two curves.
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