AP Calculus AB · Topic 6.2
Approximating Areas with Riemann Sums Practice
Part of Integration and Accumulation of Change.(FUN-5.B)
Practice questions
18
Sample questions
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Sample 1difficulty 2/5
The rectangles shown represent which Riemann sum approximation?
- A
Trapezoidal
- B
Right endpoint
- C
Midpoint
- Dcheck_circle
Left endpoint
Why
Each rectangle's height is determined by the function value at its left edge, so it is a left Riemann sum.
- A
Sample 2difficulty 2/5
The right Riemann sum on this <strong>increasing</strong> function gives
- A
An underestimate
- B
Exactly the integral
- Ccheck_circle
An overestimate
- D
The same as the midpoint rule
Why
Right endpoints have higher -values when is increasing → rectangles top above curve → overestimate.
- A
Sample 3difficulty 2/5
The Riemann-sum rectangles shown approximate . As the number of rectangles increases,
- A
Width stays the same
- B
The estimate diverges
- Ccheck_circle
The estimate converges to the exact integral
- D
Sum doubles
Why
Definition of the Riemann integral.
- A
Sample 4difficulty 2/5
The rectangles shown represent which type of Riemann sum?
- Acheck_circle
Right endpoint
- B
Midpoint
- C
Left endpoint
- D
Lower sum
Why
Each rectangle's height is determined by the function value at its right edge.
- A
Sample 5difficulty 3/5
For an increasing function, the right Riemann sum is:
- A
An underestimate
- Bcheck_circle
An overestimate
- C
Cannot be determined
- D
Exact
Why
The right endpoint gives the maximum on each subinterval for increasing , so the sum overestimates.
- A