Continuous function double integral

[humble kiln]

Got false but need confirmation

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[ripe meadow]

Try drawing the region.

[ripe meadow]

Well, you don't need to draw two of them.

The region is:
x^3 < y < x^2
0 < x < 1
Now, what would it look like if we reversed the order?

[humble kiln]

It's the same?

The shape of curves still same but region kinda flipped right?

[ripe meadow]

Well, the region is the same, but would you define it using limits for x first, then limits for y?

[humble kiln]

Limits for y?

[ripe meadow]

Well, clearly, √(x) < y < x^(1/3). What about x?

[humble kiln]

What about x?

[ripe meadow]

What will be the limits for x?

[humble kiln]

Oh

-1 to 1

[ripe meadow]

No.

[humble kiln]

Why?

[ripe meadow]

Well, the upper limit is 1.

Why should the lower limit be -1, though?

[humble kiln]

Oh it's zero

[humble kiln]

I refer to this

[ripe meadow]

Yes.

So, is the given equality correct?

[humble kiln]

No, because it's given -1 to 1 instead of 0 to 1?

[ripe meadow]

Yeah.

[humble kiln]

Owh I seee

Think I get it now, thanks!