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# c3 trig question Watch

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1. 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
2. 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)
3. well it's really a standard result

analogous to

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 , then it's slope gets less negative until it's slope is 0 at the point . (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 () and then less positive until we hit a value of 0 at . 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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