Riemann Sums

Conceptual

100

On a time-velocity graph, what does the area under a curve calculate? 

The total distance an object travels? 

200

How does subinterval # impact accuracy? 

As the number increases so does accuracy. 

300

When given # of subintervals, what is the formula to calculate base length (rectangle width). 

Base Length = (upper x - lower x) / # of subintervals. 

400

What is the most accurate Riemann Sum type? 

Trapezoid

Left

100

When used with an exponentially increasing curve, what kind of approximation will this be?

Underapproximation

200

When used which x value extreme is omitted? 

Lower

300

y = x³ + 4x² + 3

Calculate the area from -2 to 16 using LRAM with 3 subintervals. 

9270

400

y = (√x) + 8

Calculate the area using LRAM from 4 to 16 with 6 subintervals. 

131.293

500

Given the following integral: 

₂ƒ⁸ 2x + sinx dx

Calculate the area using LRAM with 3 subintervals. 

48.419

Midpoint

100

What is MRAM in relation to RRAM and LRAM? 

It is the average of RRAM and LRAM. 

200

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

300

y = x²

Using MRAM calculate the area from 0 to 5 with 5 subintervals. 

41.25

400

y = (√x) + 5

Calculate the area using MRAM from 4 to 14 using 5 subintervals. 

79.608

500

Given the following integral: 

_-5ƒ¹⁰ x² + 6x + 36 dx

Calculate the area using MRAM with 5 subintervals. 

1197.75

Right

100

When used with an exponentially increasing curve, what kind of approximation will this be?

Overapproximation

200

When used which x value extreme is omitted?

Upper

300

y = (x² ÷ 12) + 5

Using RRAM, calculate the area from 0 to 10 using 10 subintervals.  

76.999

400

y = (x³ ÷ 16) + 8

Using RRAM, calculate the area from -2 to 6 with 4 subintervals. 

100

500

Given the following integral: 

₁ƒ³ x³ - 3 dx

Calculate the area using RRAM with 4 subintervals. 

21

Trapezoid

100

What is the formula to calculate each trapezoid area? 

A = (Base 1 + Base 2) / 2 • h

200

When used with a concave up curve, what kind of approximation will this be? 

Overapproximation

300

y = (x² ÷ 4) + 6

Calculate the area from -5 to 2 using 4 subintervals. 

31.8255

400

y = 5cosx + sinx²

Calculate the area from -3 to 5 with 5 subintervals. 

39.9751