Simpsons rule question (1 Viewer)

[philthy]

I have attached a question from our trial....

I understand simpsons rule, but its the values i can't get in this question... can someone please explain to me how to get the values for that cosec function?

Cheers!

 

[wrxsti]

nice question. I changed cosec to 1/sin, got a syntax error, no help from me, sry mate, anyone else??

 

[frankyd]

Ok this is my working for it:

cosec(x.pi/6) = 1/sin(x.pi/6)

table of values:

x=1, y= 1/sin(pi/6) = 1/(1/2) = 2

x = 2, y = 1/sin(2pi/6) = 1/sin(pi/3) = 1/([root3]/2) = 2/[root3]

x = 3, y = 1/sin(pi/2) = 1/1 = 1

ok so then to the simpsons rule formula:

integral of cosec(x.pi/6) between x=1 and x=3 with 3 function values:
(using h/3(first + last + 4(odds) + 2(evens) method)

approx = (1/3){2 + 1 + 4(2/[root3])}

= 3/3 + 8/(3[root3])

= 1 + 8[root3]/9 - just rationalised the denominator here

wats the answer supposed to be?

 

[wrxsti]

wtf i think urs a problem

1/sin (pi/6) turns out to be 109.43 (to 2 dec pl)

how did you get 2???.............

 

[wrxsti]

wtf i think urs a problem

1/sin (pi/6) turns out to be 109.43 (to 2 dec pl)

how did you get 2???.............

 

[SoulSearcher]

1/sin(pi/6) = 1/sin30 = 1/(1/2) = 2

 

[wrxsti]

ooops sry, lol thxx

 

[PC]

Cosec is the reciprocal function for sine. So cosec f(x) is just 1/[sin f(x)].

Trap rule and Simmo's rule are so easy! Use a table.

x******f(x)**********W*********P
1******2.0000*******1********2.0000
2******1.1547*******4********4.6188
3******1.0000*******1********1.0000
****************************----------
*****************************7.6188

Therefore Integral = 1/3 x h x Sum
= 1/3 x 1 x 7.6188
= 2.5396

For trapezoidal rule, W (weighting) goes 1, 2, 2, 2, ...., 1 and the final approximation is 1/2 x h x sum (h is the difference between function values).

For simpson's rule, W goes 1, 4, 2, 4, 2, ...., 1 and the final approximation is 1/3 x h x sum.

Easy!

Sorry about all the stars ... hypertext doesn't like multiple spaces.

 

[fishy89sg]

there was a nice Q in the hsc once about trig functions, something like find the volume of the solid when y = sec x is revolved about the x axis between some values