Approximate areas with Riemann sums

A cyclist is cycling downhill. He recorded his instant speed every  seconds. His speed for the first  seconds is listed above. 

Approximately what is the distance he traveled in  seconds? Solve this using the right-hand sum.

A cyclist is cycling downhill. He recorded his instant speed every  seconds. His speed for the first  seconds is listed above. 

Approximately what is the distance he traveled in  seconds? Solve this using the trapezoidal sum.

A cyclist is cycling downhill. He recorded his instant speed every  seconds. His speed for the first  seconds is listed above. 

We calculate the distance traveled based on the data using left-hand sum, right-hand sum, and trapezoidal sum. We label the results as  for the right-hand sum,  for the left-hand sum, and  for the trapezoidal sum.

What is the correct order of the sums, , , and , as time goes on?

Using the trapezoidal sum, how do you calculate the areas below  and x-axis, in the interval  given that the interval was split into  blocks? 

Using the trapezoidal sum, how do you calculate the areas below  and x-axis, in the interval  given that the interval was spit into  blocks?

Using the left-hand sum, how do you calculate the areas below  and x-axis, in the interval  given that the interval was split into  blocks?

A cyclist is cycling downhill. He recorded his instant speed every  seconds. His speed for the first  seconds is listed above. 

Approximately what is the distance he traveled in  seconds? Solve this using the left-hand sum.

Using the mid-point sum, how do you calculate the areas below  and x-axis, in the interval  given that the interval was split into  blocks?

Using the mid-point sum, how do you calculate the areas below  and x-axis, in the interval  given that the interval was split into blocks?

We use Riemann sum to calculate the area below the curve  and above the x-axis, between  and .

What is the correct statement about the right-hand sum and left-hand sum?

We use Riemann sum to calculate the area below the curve  and above the x-axis, between  and .

What is the correct statement about the right-hand sum and left-hand sum?

Using the left-hand sum, how do you calculate the area below the curve  and above the x-axis, between  and  given that the interval was split into  blocks?

Using the right-hand sum, how do you calculate the area below the curve  and above the x-axis, between  and , given that the interval was split into  blocks?

Using the right-hand sum, how do you calculate the area below the curve  and above the x-axis, between  and  given that the interval was split into  blocks?

Using the left-hand sum, how do you calculate the area below the curve  and above the x-axis, between  and  given that the interval was split into  blocks?