integral from 0 to 6pi, 7theta^2(sin(1/12theta))dtheta

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integral from 0 to 6pi, 7theta^2(sin(1/12theta))dtheta

Mathematics
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integration by parts pull out the constant 7 first u = x^2 dv = sin(x/12) du = 2xdx v = -12sin(x/12)
\[\int\limits_{0}^{6\pi} 7 \theta^2 \sin(\frac{1}{12} \theta) d \theta\] ??
or is that (7t)^2 ??

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its right the first way u have it
= -12x^2cos(x/12) +24[integral xcos(x/12) dx] repeat integration by parts u = x dv = cos(x/12) du=dx v = 12sin(x/12)
if i gotta repeat integrations; i just make a table to keep them organized
if you express sin theta in eular's form then the integration will be easied
yeh, but no one wants complex numbers in the answer geezzz
v up ------------------------ u down | sin(t/12) ------------------------- + | t^2 | -cos(t/12) /12 ------------------------- - | 2t | -sin(t/12) / 144 ------------------------- + | t | cos(t/12)/ 144(12) ------------------------- 0 right?
not to forget the 7 tho lol
- 7t^2 cos(t/12) /12 + 14t sin(t/12) / 144 + 7t cos(t/12)/ 144(12) i think
amistre when you integrated the sin and cos, you multiplied the inside instead of dividing integral sin(ax) = -1/a*cos(ax) =7[-12x^2 cos(x/12) + 288x sin(x/12) + (24)(144)cos(x/12)]
still rusty at integration by parts; thnx :)
no problem table is good idea though
i seen the 12 and forgot it was a fraction :)
thanks guys :)
The derivative of \[7 \left(-1728 \left(-2+\frac{t^2}{144}\right) \text{Cos}\left[\frac{t}{12}\right]+288 t \text{Sin}\left[\frac{t}{12}\right]\right) \]is\[7 \left( 288 \text{ Sin}\left[\frac{t}{12}\right]+144 \left(-2+\frac{t^2}{144}\right) \text{Sin}\left[\frac{t}{12}\right]\right) \]simplified,\[7 t^2 \text{Sin}\left[\frac{t}{12}\right] \] The truth be told, I don't know how they did it.
can u find the answer to integral of e^(6x) cos(7x)
hold on.
\[\int\limits e^{6 x} \text{Cos}[7 x]dx = \frac{1}{85} e^{6 x} (6 \text{Cos}[7 x]+7 \text{Sin}[7 x])+c \]Does OK?
yes, thank u so much :)
You might consider buying a Student version of Mathematica 8 if you intend to pursue a scientific or math career. At least you can verify your answers.
there is wolframam alpha, google it, you can check answers on that for free

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