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I have an example in my studies as follows:

If v = 200sin(100pi*t + 0.2) then evaluate Integral of v^2 dt between limits of 0.005 and 0.

I have integrated it and used the double compound angle formula sin^2 A=1-cos2A and come up with the following as per the solution to the example in the home work studies:

20000 [t - (sin(200pi*t + 0.4)/200pi) ] ... so far so good I think.

However when I put the limits in it I get

20000 [0.005 - (sin(200pi*0.005 + 0.4)/200pi)) - (0 - (sin(200pi*0 + 0.4)/200pi)) ]

This I calculate as 20000 (0.005 + 0.0061) - (0 -0.0061) = 344

According to the solution and online examples the answer should be124.8

The solution with the limits calculated shows 20000 [ (0.005+0.00062) - (0 - 0.00062)] but I can't get these figures from what I have above. Please can anyone see where I am going wrong? It is driving me mad!

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# Integration where am I going wrong?

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