Conceptual
On a time-velocity graph, what does the area under a curve calculate?
The total distance an object travels?
When used with an exponentially increasing curve, what kind of approximation will this be?
Underapproximation
What is MRAM in relation to RRAM and LRAM?
It is the average of RRAM and LRAM.
When used with an exponentially increasing curve, what kind of approximation will this be?
Overapproximation
What is the formula to calculate each trapezoid area?
A = (Base 1 + Base 2) / 2 • h
How does subinterval # impact accuracy?
As the number increases so does accuracy.
When used which x value extreme is omitted?
Lower
Say a Riemann Sum is being set up on the interval of 3 to 5. The determined x values based on subinterval number/base length come out to be 3.5, 4, 4.5, and 5. With MRAM what will the used x values be?
3.25, 3.75, 4.25, 4.75
When used which x value extreme is omitted?
Upper
When used with a concave up curve, what kind of approximation will this be?
Overapproximation
When given # of subintervals, what is the formula to calculate base length (rectangle width).
Base Length = (upper x - lower x) / # of subintervals.
y = x3 + 4x2 + 3
Calculate the area from -2 to 16 using LRAM with 3 subintervals.
9270
y = x2
Using MRAM calculate the area from 0 to 5 with 5 subintervals.
41.25
y = (x2 ÷ 12) + 5
Using RRAM, calculate the area from 0 to 10 using 10 subintervals.
76.999
y = (x2 ÷ 4) + 6
Calculate the area from -5 to 2 using 4 subintervals.
31.8255
What is the most accurate Riemann Sum type?
Trapezoid
y = (√x) + 8
Calculate the area using LRAM from 4 to 16 with 6 subintervals.
131.293
y = (√x) + 5
Calculate the area using MRAM from 4 to 14 using 5 subintervals.
79.608
y = (x3 ÷ 16) + 8
Using RRAM, calculate the area from -2 to 6 with 4 subintervals.
100
y = 5cosx + sinx2
Calculate the area from -3 to 5 with 5 subintervals.
39.9751
Given the following integral:
2ƒ8 2x + sinx dx
Calculate the area using LRAM with 3 subintervals.
48.419
Given the following integral:
-5ƒ10 x2 + 6x + 36 dx
Calculate the area using MRAM with 5 subintervals.
1197.75
Given the following integral:
1ƒ3 x3 - 3 dx
Calculate the area using RRAM with 4 subintervals.
21