approximate integral

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July 31st 2006, 03:17 PM
norivea

Help needed!

I really need some help answering the following question. There is an example of how it should be completed but I don't understand it. The example has a diagram and advises the use of either Trapezium rule or Simpson's rule.

Question: Use a numerical method to find the area enclosed by the graph of y = x² sin x, the x axis and the lines x = 1 and x = 2.
Use an interval of 0.4

Thank you for your help!
July 31st 2006, 06:59 PM
ThePerfectHacker

Quote:

Originally Posted by norivea

I really need some help answering the following question. There is an example of how it should be completed but I don't understand it. The example has a diagram and advises the use of either Trapezium rule or Simpson's rule.

Question: Use a numerical method to find the area enclosed by the graph of y = x² sin x, the x axis and the lines x = 1 and x = 2.
Use an interval of 0.4

Thank you for your help!

For example use 4 divisions.
Then,
$\Delta x=\frac{2-1}{4}=.25$
Thus, (by trapezoid rule),
$.5[f(1)+2f(1.25)+2f(1.5)+2f(1.75)+f(2)]\times .25$
You can do the calculations.
August 1st 2006, 01:12 AM
norivea

1 Attachment(s)

So just for further clarification, I have attached my answer to this post. The area is 4.5248 with n=10 by Trapezium Rule. When you increase the n, or decrease the interval h, the area will be approaching to the real value.
When n=100, the area is 4.5360
When n=1000, the area is 4.5361

Is this correct?
August 1st 2006, 02:37 AM
CaptainBlack

Quote:

Originally Posted by norivea

So just for further clarification, I have attached my answer to this post. The area is 4.5248 with n=10 by Trapezium Rule. When you increase the n, or decrease the interval h, the area will be approaching to the real value.
When n=100, the area is 4.5360
When n=1000, the area is 4.5361

Is this correct?

What is K in your image file?

RonL
August 1st 2006, 05:11 AM
earboth

Hello, norivea,

according to the image of your reply

Quote:

Originally Posted by norivea

...
Question: Use a numerical method to find the area enclosed by the graph of y = x² sin x, the x axis and the lines x = 1 and x = 2.
Use an interval of 0.4...

the x-value shoul read 2.6 . Then the given interval make some sense.

I presume that the K in your image means "continueing"?

Greetings

EB