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Trapezium Rule

Can someone please help with this...

Using the trapezium rule with 5 ordinates, find an approximate value for:

Int(between pi/3 and 0) (1/1+ tanx) dx

Reply 1

nuodai

5 ordinates means 4 intervals. What specifically are you stuck on? Have you worked out the values of x you need to evaluate the function at?

Reply 2

mc_ragz

Original post by nuodai

5 ordinates means 4 intervals. What specifically are you stuck on? Have you worked out the values of x you need to evaluate the function at?

Just integrating the (1/1+tanx) bit...

I've turned it into 1 / ( 1 + sinx/cosx) dx...but then I don't know what to do :s

Reply 3

dknt

Original post by mc_ragz

Just integrating the (1/1+tanx) bit...

I've turned it into 1 / ( 1 + sinx/cosx) dx...but then I don't know what to do :s

You don't integrate when using the trapezium rule... that's kind of the point of using the trapezium rule.

Reply 4

nuodai

Original post by mc_ragz

Just integrating the (1/1+tanx) bit...

I've turned it into 1 / ( 1 + sinx/cosx) dx...but then I don't know what to do :s

This is a trapezium rule question, not a direct integration question; you don't integrate and evaluate, you estimate (using the trapezium rule).

This integral can be evaluated directly, but not at C2 level.

(edited 12 years ago)

Reply 5

mc_ragz

ok so I just realised how stupid I was being, thanks for pointing it out for me guys lol..

(edited 12 years ago)

Reply 6

nuodai

Original post by mc_ragz

Oh yeah :s but how do I do this question :s I'm stuck...

The trapezium rule states that

\displaystyle \int_a^b f(x)\, dx = \dfrac{b-a}{2n} ( y_0 + 2y_1 + 2y_2 + \cdots + 2y_{n-1} + y_n)

where you split the interval

a<x<b

into

n

even strips, where

y_k = f(x_k)

is your function evaluated between each strip.

You should already know how to use the trapezium rule if you've been set a question on it. Look at your textbook if you're still confused -- this question is no different to any others.

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Trapezium Rule

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