Integration Help: Questions & Answers

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Homework Statement


http://img19.imageshack.us/img19/723/43674288.jpg


Homework Equations





The Attempt at a Solution


1. what's the difference between integrand and definite integral?
2. can you tell me if so far i did everything correct or not.
3. would the 3rd one be I?
4. function of f? i have no idea.. no of the options seem to fit in.. :|
 
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you should be able to answer the rest by elimination knowing that what you have done is correct and yes what you have done is correct.

the integrand is what you are integrating.

you have 10 questions on the left side so you need to use something twice... 3ed one is a duplicate.
 
for the 3rd one i put 'I' and for the 'function f' i put C...
and its wrong..
as you said: "the integrand is what you are integrating. " so I am integrating the function f so it must be 'C'
 
The function f is the integrand. The third one is most certainly not "I" however. Think about the definition of a definite integral.
 
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yes you picked the wrong duplicated. when you take the limit as n goes to infinity something special happens to the Riemann sum and it becomes the definition of the definite integral.
 
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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