- #1
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Homework Statement
Using the macluarin's expansion for sinx show that [itex]\int sinx dx=-cosx+c[/itex]
Homework Equations
[tex]sinx=\sum_{n=0} ^\infty \frac{(-1)^nx^{2n+1}}{(2n+1)!}[/tex]
The Attempt at a Solution
Well I can easily write out some of the series and just show that it is equal to -cosx
but if I integrate the representation for the infinite series i get
[tex]\int sinx dx= \sum_{n=0} ^\infty \frac{(-1)^nx^{2n+2}}{(2n+1)!}[/tex]
shouldn't -cosx be:
[tex]\int sinx dx= \sum_{n=0} ^\infty \frac{(-1)^{n+1}x^{2n+2}}{(2n+1)!}[/tex]
and also I am supposed to get [itex]x^{2n}[/itex] not what I got