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    does sin (2x - 1) intergrate to (-1/2) cos(2x-1)

    Im pretty sure it dos but i dont understand why the -1 doesnt come into the equation.

    i know the sinkx > -1/k sinkx
    But could you not take it as cosx as the (2x-1) is in brackets, so it could become -cos(2x-1)

    Im confused :P
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    Yeah i think you're right.
    The -cos differentiates to sin, and the 1/2 is multiplied by 2 (from 2x-1) to give you 1.

    So yeah, as far as i can tell sin(2x-1) intergrates to -1/2 cos(2x-1)
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    well it's really a standard result

    \int \sin{(ax+b)} dx = -\frac{1}{a} \cos{(ax+b)}

    analogous to \int \sin{x} dx= - \cos{x}

    as for the reason why, well imagine a cos graph at a very small, positive x value, what is the slope fo the curve like? well it's negative certainly and it gets increasingly more negative up to a point \frac{\pi}{2}, then it's slope gets less negative until it's slope is 0 at the point \pi. (It may take a bit of thought to trace this but if you read it whilst looking at a cos graph you should see what I'm on about. Anyway we know the sine graph gets increasingly positive up to a point (\frac{\pi}{2}) and then less positive until we hit a value of 0 at \pi. SO if we put a minus sign in front of the sin, it will all work out as required!

    Hope this helps.
 
 
 
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