Maths Portfolio Shady Areas

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Shady Areas

Standard Level

Name Anis Mebarek

Candidate Number:

Shady areas:

We are able to find the area under the graph through calculating the area of the trapeziums under it. Through having numerous trapeziums under the curve the amount of uncertainty within the answer decreases this is due to the uncalculated area decreasing. I will be investigating and proving this theory from using the function and to find out the area of the trapezium I will use this formula .

As seen from the graph the area between the curve and the trapezium is also being calculated when trying to find the area under the line therefore we are expected to get a higher number then the area it's self. But increasing the number of trapeziums on the graph from 1 to 2, the uncertainty for area decreases. This can be seen from the graph below.

Therefore through increasing the number of trapeziums within the graph the uncertainty of the answer will decreases and so will the number for the area will decrease, as the trapeziums will over-estimate the number for the area. To prove this I will have to calculate the