Approximating Area

Which of the following methods is most accurate?

• Left Riemann sum
• Midpoint Riemann sum
• Right Riemann sum

What type of Riemann sum is shown?

• Left Riemann sum
• Midpoint Riemann sum
• Right Riemann sum
• None of the Above

What type of Riemann sum is shown?

• Left Riemann sum
• Midpoint Riemann sum
• Right Riemann sum
• None of the Above

What type of Riemann sum is shown?

• Left Riemann sum
• Midpoint Riemann sum
• Right Riemann sum
• None of the Above

Which is an expression for the midpoint Riemann sum?

• 2⋅f(0)+2⋅f(2)+2⋅f(4)+2⋅f(6)
• 2⋅f(2)+2⋅f(4)+2⋅f(6)+2⋅f(8)
• 2⋅f(1)+2⋅f(3)+2⋅f(5)+2⋅f(7)
• All are acceptable ways of finding the midpoint sum

Which is an expression for the right Riemann sum?

• 2(f(0)+f(2)+f(4)+f(6))
• 2(f(2)+f(4)+f(6)+f(8))
• 2(f(1)+f(3)+f(5)+f(7))

Approximate the area between the x-axis and g(x), from x = 10 to x = 16 using a LEFT Riemann sum with 3 unequal subdivisions.

• 10 units²
• 15 units²
• 20 units²
• 35 units²

If you used a Left Riemann sum on this function (same as the previous question), is it an over or under estimate?

• Overestimate
• Underestimate
• Neither
• Both

Approximate the area between the x-axis and h(x) =x³+2 from x=-1 to x=5 using a RIGHT Riemann sum with 3 equal subdivisions.

• 152 units²
• 273 units²
• 318 units²
• 416 units²

If you used a Right Riemann sum on this function (same as the previous question), is it an over or under estimate?

• Overestimate
• Underestimate
• Neither
• Both