$C[-\pi, \pi], f(x)=x$ and $g(x)= \cos 2x$ I am having a difficulties integrating this function. I dont know where I am messing up. Please help me :D
Find the Orthogonal Projection of f onto g. Use the inner product in C[a,b]
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linear-algebra
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0and I don't know, what you mean? Maybe $\int_{-\pi}^\pi x\cos 2x dx$? This is $0$, do you know why$ – 2012-02-27
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0well idk latex but I will show u the formula – 2012-02-27
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)/( – 2012-02-27)g -
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is what u have showed but i don't get know how to integrate that function – 2012-02-27 -
0ohh i see. ya I get it now soit orthogonal already ok thanks @draks – 2012-02-27
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0@Sarah For the good of mankind and all that is sacred, please spell "you" as "you" and not "u". Note also that "i" should be capitalized as "I". Furthermore, since "Dont" is a contraction, please consider writing it as "Don't". Finally, although I know that "idk" is an abbreviation for "I don't know", I'm not so sure non-native speakers of English would realize that. – 2012-02-27
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0haha ok. I guess I this site isn't meant for me @3sphere – 2012-02-27
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0@Sarah I did not intend to imply that, only that a reasonable effort at grammatical correctness is appreciated. – 2012-02-27
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0I'm glad, if I could help. – 2012-02-27
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0Yes, you are correct. Sorry about that.@3Sphere – 2012-02-27
1 Answers
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Here are three approaches for calculating $\int_{-\pi}^\pi x\cos 2x$. These are only hints, as this is a homework problem:
- Use integration by parts, by defining $f(x)=x,\ g(x)=\cos 2x$.
- Use the fact that the integrand is an odd function of $x$. What is the integral of an odd function on a segment that is symmetric around $0$?
- Ask Wolfram Alpha and click "show steps".
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0Thanks @yohBS That was helpful – 2012-02-27