hi.
i've jux come across calculating the exact same integral (except that it's definite!). i tried to solve it using different substitutions bt all in vain. So. culd somebody post the complete solution here.
Exercise 9d Q2(d) of this book:
http://books.google.com.pk/books?id=gB5QyMiCOGsC&pg=PA294&dq=zFurther+Pure+Maths&hl=en&ei=wy-VTNazLovJcfbivKQF&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC4Q6AEwAQ
Here is an attachment to the question:
https://www.physicsforums.com/showthread.php?t=430362
Homework Statement
Find the values of Σ(a^2), Σ(1/a), Σ(a^2)(B^2) and ΣaB(a + B) for: x^4 - x^3 + 2x + 3 = 0
Homework Equations
Σa = 1, ΣaB = 0, ΣaBC = -2, aBCD = 3
The Attempt at a Solution
I found the Σ(a^2) and Σ(1/a) successfully correct bt could neither find Σ(a^2)(B^2)...
We want to show that
Σ(n=1 to N) sin(nθ) / 2^n = [2^(N+1) sin θ + sin (Nθ) - 2 sin(N+1)θ] / [2^N (5 - 4 cos θ)].
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Note that e^(iθ) = cos θ + i sin θ.
So, De Moivre's Theorem yields for any positive integer n
e^(inθ) = (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ)...
Can some1 post the whole solution? How to get the 2^N[5-4Cos(theta)]
How do we get cos? If we are taking the imaginry part? Please solve it and post it... thanks in advance