Question

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

Answer 1

integration by parts
pull out the constant 7 first
u = x^2 dv = sin(x/12)
du = 2xdx v = -12sin(x/12)

Answer 2

\[\int\limits_{0}^{6\pi} 7 \theta^2 \sin(\frac{1}{12} \theta) d \theta\] ??

Answer 3

or is that (7t)^2 ??

Answer 4

its right the first way u have it

Answer 5

= -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)

Answer 6

if i gotta repeat integrations; i just make a table to keep them organized

Answer 7

if you express sin theta in eular's form then the integration will be easied

Answer 8

yeh, but no one wants complex numbers in the answer geezzz

Answer 9

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?

Answer 10

not to forget the 7 tho lol

Answer 11

- 7t^2 cos(t/12) /12 + 14t sin(t/12) / 144 + 7t cos(t/12)/ 144(12) i think

Answer 12

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)]

Answer 13

still rusty at integration by parts; thnx :)

Answer 14

no problem
table is good idea though

Answer 15

i seen the 12 and forgot it was a fraction :)

Answer 16

thanks guys :)

Answer 17

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.

Answer 18

can u find the answer to integral of e^(6x) cos(7x)

Answer 19

hold on.

Answer 20

\[\int\limits e^{6 x} \text{Cos}[7 x]dx = \frac{1}{85} e^{6 x} (6 \text{Cos}[7 x]+7 \text{Sin}[7 x])+c \]Does OK?

Answer 21

yes, thank u so much :)

Answer 22

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.

Answer 23

there is wolframam alpha, google it, you can check answers on that for free