2 nd Problem of Calculus – Area. Sigma Notation Examples.

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Presentation transcript:

2 nd Problem of Calculus – Area

Sigma Notation Examples

Summation (Sigma) Formulas

Example

Find Area Between a Curve and X-axis

x f(x)

Most people don't know that polar bears live in igloos they build each year. To build an igloo, they find a large field of snow and flatten it down so the snow is compressed sufficiently. Next, they cut blocks of snow from this field and build igloos by layering the block in smaller and smaller rings until they have formed their structure. It takes approximately 100 blocks of snow to form one igloo. Trapezoid Example

This year they came upon a field which they had to measure using calculus. Blocks are measured in "cubic bears" and length is measured in "bears". Basically, a block of snow to make an igloo is 1/8 of a bear wide and 1/4 of a bear long. The height of the block corresponds to the depth at which they cut into the snow and therefore does not impact this problem. The field of snow they used this year was divided up into subintervals of 4 bear units. The length of the field was measured at each interval and the following distances were calculated: Location of measurement Left endpt 2 nd value 3 rd value 4 th value 5 th value 6 th value 7 th value 8 th value Right endpt Measurement

Location of measurement Left endpt 2 nd value 3 rd value 4 th value 5 th value 6 th value 7 th value 8 th value Right endpt Measurement (bear units)

Review – Approximating Areas