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

NameDate

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

Esme estimates the area under f(x) = x² + 2 from x = 0 to x = 6 with 3 rectangles, using right ends. What is the estimate?
Jun estimates the area under f(x) = x² + 3 from x = 0 to x = 2 with 4 rectangles, using right ends. What is the estimate?
Kira estimates the area under f(x) = x² + 1 from x = 0 to x = 9 with 3 rectangles, using right ends. What is the estimate?
Luz estimates the area under f(x) = x² + 5 from x = 0 to x = 4 with 2 rectangles, using right ends. What is the estimate?
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Values of f (example values)
x f(x)
0 1
1 2
2 4
3 7
4 11
5 16
6 22
Milo estimates the area under f from x = 0 to x = 6 with three equal strips and midpoint heights (see the table). What is the estimate?
Ren estimates the area under f from x = 0 to x = 12 with three equal strips and midpoint heights (see the table). What is the estimate?
Tala estimates the area under f from x = 0 to x = 6 with three trapezoids (see the table). What is the estimate?
Pia estimates the area under f from x = 0 to x = 12 with three trapezoids (see the table). What is the estimate?
Bo estimates the area under f from x = 1 to x = 7 with three trapezoids (see the table). What is the estimate?
Ari estimates the area under f from x = 0 to x = 3 with three trapezoids (see the table). What is the estimate?

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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