Triple Integral of ysinx: Evaluating Limits and Solving for the Solution

joemama69
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Homework Statement



evaluate ysinx from z= 0 to (1-y2)1/2, y = 0 to 1, x = 0 to pi

Homework Equations





The Attempt at a Solution



heres my work

-1/2sinx \int(1-y^2)^1/2 y dy from 0 to 1 =
\int1/3*sinx dx from 0 to pi = 2/3

Homework Statement

 
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Thread 'Finding the nth roots of a complex number'

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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