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Math Help - Piecewise Integral, question about breaking integrals up

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    Piecewise Integral, question about breaking integrals up

     \int_{-\pi}^{\pi} f(x)dx where f(x) = \left\{ {\begin{array}{rl}   {6x^3,} & {\text{if }x~-\pi=<x<0}  \\   {7sin(x),} & {\text{if }x~0=<x<=\pi}  \\\end{array} } \right.

    I broke up the integral like this  \int_{-\pi}^{0} 6x^{3} dx + \int_{0}^{\pi} 7sin(x) . When I look at the graph of these two functions I notice that they overlap each other. Does that affect the area value in any way? I know the antiderivates will be even functions, so I think I only have to find the integral of the 1st and 4th quadrant and then just double it. If I do :  2 \int_{0}^{\pi} 7sin(x) I get 28, but that's not correct. I'm sure I'm just not understanding something about these graphs, that's what I ask if the overlap feature means I need to break up the endpoints of the integral differently?
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    Re: Piecewise Integral, question about breaking integrals up

    Quote Originally Posted by AZach View Post
     \int_{-\pi}^{\pi} f(x)dx where f(x) = \left\{ {\begin{array}{rl}   {6x^3,} & {\text{if }x~-\pi=<x<0}  \\   {7sin(x),} & {\text{if }x~0=<x<=\pi}  \\\end{array} } \right.


    I do not understand most of your statement. In particular the bit about "overlapping".

    Look at this graphic.
    Attached Thumbnails Attached Thumbnails Piecewise Integral, question about breaking integrals up-untitled.gif  
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    Re: Piecewise Integral, question about breaking integrals up

    When I graphed the two functions 6x^3 and 7sin(x) on my TI83 I got a graph that looked like this Piecewise Integral, question about breaking integrals up-piecewise-graph.jpg

    Did I have the integrals broken up correctly?
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    Re: Piecewise Integral, question about breaking integrals up

    Quote Originally Posted by AZach View Post
    When I graphed the two functions 6x^3 and 7sin(x) on my TI83 I got a graph that looked like this Click image for larger version. 

Name:	Piecewise graph.jpg 
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    Did I have the integrals broken up correctly?
    6x^3 is for x < 0 and 7\sin{x} is for x \ge 0 ... they do not "overlap".

    how to graph this piece-wise function in a TI-83 ...

    Y1 = 6x^3/(x < 0)

    Y2 = 7\sin(x)/(x \ge 0)

    set your x window from -\pi to \pi and y window from -10 to 10
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    Re: Piecewise Integral, question about breaking integrals up

    Thanks Skeeter, I never knew how to do that before.
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