# Thread: change of variable for multiple integration. no known transformation.

1. ## change of variable for multiple integration. no known transformation.

I am trying to find a transformation that will convert the region bounded by y=0 and y=(1+x^6)^1/6 to a region that is a rectangle.

2. On what interval?

3. The point is that those two curves do NOT bound a finite region.

4. Okay I cannot write things down. The second curve is y=(1-x^6)^1/6 so it bounds on x between -1 and 1 and y between 0 and 1. But I cannot integrate most functions with the above expression as a bound on my finite integral.

5. If you're trying to transform the region bound by

$y = 0, y = (1+x^6)^{1/6}, x = -1 \; \text{and}\; x = 1$

to say a rectangle, try the transformation

$u = x,\;\; v = \dfrac{y}{(1+x^6)^{1/6}}$.