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Area Between Curves - Worksheet 5 - 12th Grade

Medium

Compute exact integrals and sums, distinguish area from signed integrals, and include constants for indefinite integrals.

medium: Use shifts, products or multiple terms.

14 problems · 30-35 minutes · Skills: integrals, area, applications

About This Worksheet

This medium-level worksheet contains 14 problems designed for 12th Grade students practicing area between curves. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

  • Compute exact integrals and sums, distinguish area from signed integrals, and include constants for indefinite integrals.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Find the area between y = 3x and y = 0 from x = 0 to x = 2.
Solution Steps:
  1. On this interval the line is above the x-axis.
  2. Integrate top minus bottom over the interval.
Answer: 6 square units
Tip: Check your result using the method in the example before moving to the next question.
1
Find the area between y = 2x and y = x² on [0, 2].
2
Find the area between y = 6x and y = x² on [0, 6].
3
Find the area between y = 3x and y = x² on [0, 3].
4
Find the area between y = 4x and y = x² on [0, 4].
5
Find the area between y = 1x and y = x² on [0, 1].
6
Find the area between y = 5x and y = x² on [0, 5].
7
Find the area between y = 1x and y = x² on [0, 1].
8
Find the area between y = 6x and y = x² on [0, 6].
9
Find the area between y = 3x and y = x² on [0, 3].
10
Find the area between y = 5x and y = x² on [0, 5].
11
Find the area between y = 2x and y = x² on [0, 2].
12
Find the area between y = 4x and y = x² on [0, 4].
13
Find the area between y = 3x and y = x² on [0, 3].
14
Find the area between y = 6x and y = x² on [0, 6].

Answer Key

1. 4/3 square units2. 36 square units3. 9/2 square units4. 32/3 square units5. 1/6 square units6. 125/6 square units7. 1/6 square units8. 36 square units9. 9/2 square units10. 125/6 square units11. 4/3 square units12. 32/3 square units13. 9/2 square units14. 36 square units

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What skills does this integrals worksheet cover?

This worksheet focuses on integrals, area, applications. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 14 problems. It typically takes 30-35 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.