Double integral question: Evaluating Integrals with Sinusoidal Functions

engineer_dave
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Double integral question...

Homework Statement



Evaluate the integrals shown ( I have attached the file with the integral).

Homework Equations





The Attempt at a Solution



Ok, for the first one, can you tell me how I integrate sin x^2...?? which method should i use? And for the second one, I don't really understand what the R is. What do u have to do to find the values next to to the integrand. Thanks!
 

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Can you integrate x*sin(x^2)?
 
yea but this doesn't have an x in front of it
 
any helpers lol??
 
Then I have no idea.
 
x is in the limits of the dy integration. Integrating sin(x^2) dy gives y*sin(x^2). Now put in the y limits THEN integrate dx. See, it does have an x in front of it.
 
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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