Grade 12 · Math · Calculus

12th grade Approximate area under a curve worksheet

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Approximate area under a curve

Grade 12 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

Read this first
Values of f (example values)
x f(x)
0 3
2 5
4 9
6 15
Esme estimates the area under f from x = 0 to x = 6 with three rectangles, using left ends (see the table). What is the estimate?
Kira estimates the area under f from x = 10 to x = 25 with three rectangles, using left ends (see the table). What is the estimate?
Luz estimates the area under f from x = 0 to x = 1.5 with three rectangles, using left ends (see the table). What is the estimate?
4.
Milo splits x = 0 to x = 6 into 3 equal strips for a left sum. Which heights does Milo use?
- f(0), f(2), f(4)
- f(1), f(3), f(5)
- f(2), f(4), f(6)
5.
Noah splits x = 1 to x = 9 into 4 equal strips for a right sum. Which heights does Noah use?
- f(3), f(5), f(7), f(9)
- f(2), f(4), f(6), f(8)
- f(1), f(3), f(5), f(7)
6.
Ren splits x = 2 to x = 10 into 4 equal strips for a left sum. Which heights does Ren use?
- f(3), f(5), f(7), f(9)
- f(2), f(4), f(6), f(8)
- f(4), f(6), f(8), f(10)
7.
Zee splits x = 0 to x = 3 into 3 equal strips for a right sum. Which heights does Zee use?
- f(0.5), f(1.5), f(2.5)
- f(0), f(1), f(2)
- f(1), f(2), f(3)
Tala splits the interval from x = 1 to x = 9 into 4 equal strips. How wide is each strip?
Bo splits the interval from x = −3 to x = 5 into 4 equal strips. How wide is each strip?
Ari splits the interval from x = 3 to x = 8 into 10 equal strips. How wide is each strip?

Estimate the area under a curve with rectangles and trapezoids. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

strip: One thin piece of the region, width (b − a) ÷ n.

left (right) sum: Rectangles whose heights come from each strip's left (right) end.

midpoint sum: Rectangles whose heights come from each strip's middle.

trapezoid rule: Strips topped by slanted lines: width × (left + right) ÷ 2.

Took each height at the right end of its strip. A left sum uses the left end of each strip.

Took each height at the left end of its strip, but this sum uses a different point.

Took each height at the middle of its strip, which is the midpoint sum.

What is the most common mistake with approximate area under a curve?

Took each height at the right end of its strip. A left sum uses the left end of each strip.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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