Reiman Sum and Integration

Use a right Riemann Sum to approximate the area of the shaded area.

• 12

• 9

• 10

• 5

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.

What is the approximate area of the region, using 4 subintervals and heights using left values?

• 7.5

• 7.75

• 10

• 11.5

What is the value of the Riemann sum?

• 8

• 10

• 11

• 12

What statement best describes the Riemann Sum?

• 4 intervals, with heights using middle values

• 4 intervals, with heights using left values

• 5 intervals, with heights using middle values

• 5 intervals, with heights using right values

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.) 

• 5(3) + 1(4) + 2(5) + 1(7)
• 5(4) + 1(5) + 2(7) + 1(6)
• 5(3) + 6(4) + 8(5) + 9(7)
• 0(3) + 5(4) + 6(5) + 8(7)

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

• Overestimate
• Underestimate
• Exact Solution
• Unable to Determine

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

• Overestimate
• Underestimate
• Unable to Determine
• Exact Solution

Calculate the approximation for the given function & interval.

R₃, f(x) = 7 - x, [3, 5]

• 16/3

• 5

• 26/3

• DNE

Integrate:

• x^1/2 + C

• ¹/_(2√x) + C

• ³/₂*x^3/2 + C

• ²/₃*x^3/2 + C

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2