## Reflection: Complex Tasks Area Under a Curve - Day 2 of 2 - Section 2: Extend

The second graph of the homework was a change from the ones we did together - the x-values started at -1 instead of 0. Students were setting up the equations exactly like the others and were getting an area of about one square unit - they knew that it was not reasonable.

Students were using the expression (3/4)n to represent the sequence of x-values that need to be plugged in for x to get the heights of each rectangle. When they plug in the first n-value (n = 1) they get 3/4 as the first x-value, but the first rectangle's height should occur when x = -0.25, or shifted one unit to the left.

In order to combat this, we shifted the entire graph one unit to the right. Our new equation would be y = 3 - 0.25(x - 1)^3. The area should be identical but it simplifies the process. Since we are now starting at zero, we can still use the expression (3/4)n to represent the sequence of x-values.

Complex Tasks: Changing the Graph

# Area Under a Curve - Day 2 of 2

Unit 9: Sequences and Series
Lesson 14 of 18

## Big Idea: How can we find the area of highly irregular regions?

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Standards:
Subject(s):
Math, Precalculus and Calculus, Sequences and Series, partial sum, area, limit
40 minutes