Sketch the region enclosed by the given curves. Decide whether to integrate.

phillyolly
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Homework Statement


Sketch the region enclosed by the given curves. Decide
whether to integrate with respect to x or y. Draw a typical approximating
rectangle and label its height and width. Then find the
area of the region.

Homework Equations


The Attempt at a Solution


My result gave me an answer "-20". The area cannot be negative, please check my answer for a mistake?
 

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If you want to find the area between two curves f(x) and g(x), how do you know whether to integrate f(x)-g(x) or g(x)-f(x)? Use your graph.
 
OK, I got it. This is my try. Thank you.
 

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Yes, that's right.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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