Monte Carlo integration between two lines

Hi, this is my first post here. I hope this was a suitable forum to post in.

I have a maths assignment where we have to use Monte Carlo integration to find the area of a farmland. The land is a trapezium shape, and it is divided by a river in the form of a cubic polynomial. The area to be used for farming is the land below this river.

The function for the line of the trapezium is y=5x+15, and the polynomial is y=x^3-9x^2+20x+4.

I have to create the random points using either my TI-84 Plus, MS Excel or another computer program. The problem I face is that all the points must be made within the trapezium. I've created a suitable scatter diagram in excel, but so far I've only been able to create the points within a rectangle. Is there a way I can get points to appear only within the trapezium boundary?

Re: Monte Carlo integration between two lines

Quote:

Originally Posted by

**sammoboi7321** Hi, this is my first post here. I hope this was a suitable forum to post in.

I have a maths assignment where we have to use Monte Carlo integration to find the area of a farmland. The land is a trapezium shape, and it is divided by a river in the form of a cubic polynomial. The area to be used for farming is the land below this river.

The function for the line of the trapezium is y=5x+15, and the polynomial is y=x^3-9x^2+20x+4.

I have to create the random points using either my TI-84 Plus, MS Excel or another computer program. The problem I face is that all the points must be made within the trapezium. I've created a suitable scatter diagram in excel, but so far I've only been able to create the points within a rectangle. Is there a way I can get points to appear only within the trapezium boundary?

Google rejection sampling, that is you sample uniformly on a larger easier area and reject any samples that do not fall within the more restricted area.

CB

Re: Monte Carlo integration between two lines

Cheers!

I will use that (Nod)