# Thread: Using simpsons rule integration

1. ## Using simpsons rule integration

simpsons rule... (please let me know if I've copied this wrong!!)

w/3 [(y0+yn+4(y1+y3+y5....)+2(y2+y4+y6...)]

I got my q

∫(below)0 (above)2π /3 sin x dx (4 strips)

can I please have some help??

simpsons rule... (please let me know if I've copied this wrong!!)

w/3 [(y0+yn+4(y1+y3+y5....)+2(y2+y4+y6...)]

I got my q

∫(below)0 (above)2π /3 sin x dx (4 strips)

can I please have some help??
$\int_0^{\frac{2\pi}{3}} \sin{x} \, dx = \frac{\pi}{18}\left[\sin(0) + 4\sin\left(\frac{\pi}{6}\right) + 2\sin\left(\frac{\pi}{3}\right) + 4\sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{2\pi}{3}\right)\right]
$

3. $\int_0^{\frac{2\pi}{3}} \sin{x} \, dx = \frac{\pi}{18}\left[\sin(0) + 4\sin\left(\frac{\pi}{6}\right) + 2\sin\left(\frac{\pi}{3}\right) + 4\sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{2\pi}{3}\right)\right]
$

okay see I'm getting...

$\int_0^{\frac{2\pi}{3}} \sin{x} \, dx = pi/18 [sin (0) + sin (120) + 4 (0.5 + 1) + 2(sin 120)]
$

which goes as pi/18 [0 + root3/2 + 4(1.5) + root3]

in which I get the answer as approximate to 1.5

The answer in the textbook is 3.0

I'm not sure I completely understand your working skeeter...

$\int_0^{\frac{2\pi}{3}} \sin{x} \, dx = \frac{\pi}{18}\left[\sin(0) + 4\sin\left(\frac{\pi}{6}\right) + 2\sin\left(\frac{\pi}{3}\right) + 4\sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{2\pi}{3}\right)\right]
$

okay see I'm getting...

$\int_0^{\frac{2\pi}{3}} \sin{x} \, dx = pi/18 [sin (0) + sin (120) + 4 (0.5 + 1) + 2(sin 120)]
$

which goes as pi/18 [0 + root3/2 + 4(1.5) + root3]

in which I get the answer as approximate to 1.5

The answer in the textbook is 3.0

I'm not sure I completely understand your working skeeter...
$\frac{\Delta x}{3} \left(y_0 + 4y_1 + 2y_2 + 4y_3 + y_4\right)$

$\Delta x = \frac{\pi}{6}$

$y_0 = \sin(0)$

$y_1 = \sin\left(\frac{\pi}{6}\right)$

$y_2 = \sin\left(\frac{\pi}{3}\right)$

$y_3 = \sin\left(\frac{\pi}{2}\right)$

$y_4 = \sin\left(\frac{2\pi}{3}\right)$

you have the same values as I , except you are mixing degrees with radians. don't do that.

note that you were lucky since sin(120) = sin(60) ... you listed sin(120) twice.

5. Originally Posted by skeeter
$\frac{\Delta x}{3} \left(y_0 + 4y_1 + 2y_2 + 4y_3 + y_4\right)$

$\Delta x = \frac{\pi}{6}$

$y_0 = \sin(0)$

$y_1 = \sin\left(\frac{\pi}{6}\right)$

$y_2 = \sin\left(\frac{\pi}{3}\right)$

$y_3 = \sin\left(\frac{\pi}{2}\right)$

$y_4 = \sin\left(\frac{2\pi}{3}\right)$

you have the same values as I , except you are mixing degrees with radians. don't do that.

note that you were lucky since sin(120) = sin(60) ... you listed sin(120) twice.
okay... don't mix... makes sense... but if we are still getting the same answers I must have understood something... But I'm still getting 1.5 as the value? Can I ask what are you getting when you type it all in?

okay... don't mix... makes sense... but if we are still getting the same answers I must have understood something... But I'm still getting 1.5 as the value? Can I ask what are you getting when you type it all in?
1.5 is the exact value of the integral ... you should be getting 1.500647392

simpson's rule is, after all, an approximation.

7. Originally Posted by skeeter
1.5 is the exact value of the integral ... you should be getting 1.500647392

simpson's rule is, after all, an approximation.
I'm in highschool we always go to 2 decimal places haha