Approximate areas with Riemann sums

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

Choose the correct statements 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 .

Choose the correct statements about the right-hand sum and left-hand sum.

Using the right-hand sum to calculate the area below the curve  and above the x-axis, between  and .

We split the interval into 4 blocks.

A cyclist is cycling downhill. He recorded his instant speed every 0.5 seconds. His speed for the first 3 seconds is listed above. 

Approximate the distance he traveled in 3 seconds using the left-hand sum

A cyclist is cycling downhill. He recorded his instant speed every 0.5 seconds. His speed for the first 3 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. Choose the correct order.

A cyclist is cycling downhill. He recorded his instant speed every 0.5 seconds. His speed for the first 3 seconds is listed above. 

Approximate the distance he traveled in 3 seconds using the right-hand sum

Use the trapezoidal sum to calculate the areas below  and x-axis, in the interval .

We split the interval into 4 blocks. 

Use the mid-point sum to calculate the areas below  and x-axis, in the interval .

We split the interval into 4 blocks. 

Use the trapezoidal sum to calculate the areas below  and x-axis, in the interval .

We split the interval into 4 blocks. 

Use the mid-point sum to calculate the areas below  and x-axis, in the interval .

We split the interval into 4 blocks. 

Use the left-hand sum to calculate the areas below  and x-axis, in the interval .

We split the interval into 4 blocks. 

Using the left-hand sum to calculate the area below the curve  and above the x-axis, between  and .

We split the interval into 4 blocks.

Using the right-hand sum to calculate the area below the curve  and above the x-axis, between  and .

We split the interval into 4 blocks.

Using the left-hand sum to calculate the area below the curve  and above the x-axis, between  and .

We split the interval into 4 blocks.

A cyclist is cycling downhill. He recorded his instant speed every 0.5 seconds. His speed for the first 3 seconds is listed above. 

Approximate the distance he traveled in 3 seconds using the trapezoidal sum.