Riemann Sum

What is the area of a rectangle with length a and width b?

• a + b

• ab

• a²

• b²

• 3b

• 5b

• 6b

• 9b

It is an approximate area of a region, obtained by adding up the areas of multiple simplified slices of the region.

• Riemann sum

• summation notation

• definite integral

• sum of a series

What polygon is used in the Riemann sum?

• trapezoid

• triangle

• rectangle

• rhombus

• 
• 
• 
• 

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Exact Solution
• Unable to Determine

• 17

• 44

• 53

• 15

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

Using the Left Riemann Sum, approximate the area bounded by $y=\frac{1}{4}x^2+2$  from  $x=0$  to  $x=4$  when  $n=4$ .

 

• 15.5

• 13.25

• 12.15

• 11.5