Area - Triangle Compared To Integration
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Area – Triangle Compared to Integral Assessment: worth up to +5% on one test
For Problem #1 1.
For Problem #2
What is the ratio of the orange area (the integral under x2) to the blue area (the area within the circumscribed triangle and above the integral)?
2.
What is the ratio of the orange area to the blue area?
3.
What would the ratio be if the endpoints of the entire blue/orange triangle were (0,0), (a,0), and (a, f(a)), where a > 0?
4.
Find the ratio for the function f ( x ) = bx n with triangle endpoints (0,0), (a,0), and (a, f(a)), for a,b,n > 0.
5.
As n changes, the ratio changes. How fast is the ratio changing at the moment when f is a quintic function?
Area – Triangle Compared to Integral Assessment: worth up to +5% on one test
For Problem #1 1.
For Problem #2
What is the ratio of the orange area (the integral under x2) to the blue area (the area within the circumscribed triangle and above the integral)?
2.
What is the ratio of the orange area to the blue area?
3.
What would the ratio be if the endpoints of the entire blue/orange triangle were (0,0), (a,0), and (a, f(a)), where a > 0?
4.
Find the ratio for the function f ( x ) = bx n with triangle endpoints (0,0), (a,0), and (a, f(a)), for a,b,n > 0.
5.
As n changes, the ratio changes. How fast is the ratio changing at the moment when f is a quintic function?
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