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Area Between Curves - Worksheet 1 - 12th Grade

Easy

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

easy: Apply a basic rule to simple coefficients.

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

About This Worksheet

This easy-level worksheet contains 12 problems designed for 12th Grade students practicing area between curves. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

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 = 0 from x = 0 to x = 3.
2
Find the area between y = 5x and y = 0 from x = 0 to x = 2.
3
Find the area between y = 5x and y = 0 from x = 0 to x = 1.
4
Find the area between y = 4x and y = 0 from x = 0 to x = 3.
5
Find the area between y = 4x and y = 0 from x = 0 to x = 2.
6
Find the area between y = 6x and y = 0 from x = 0 to x = 2.
7
Find the area between y = 1x and y = 0 from x = 0 to x = 2.
8
Find the area between y = 1x and y = 0 from x = 0 to x = 3.
9
Find the area between y = 3x and y = 0 from x = 0 to x = 4.
10
Find the area between y = 6x and y = 0 from x = 0 to x = 3.
11
Find the area between y = 3x and y = 0 from x = 0 to x = 5.
12
Find the area between y = 5x and y = 0 from x = 0 to x = 5.

Answer Key

1. 9 square units2. 10 square units3. 5/2 square units4. 18 square units5. 8 square units6. 12 square units7. 2 square units8. 9/2 square units9. 24 square units10. 27 square units11. 75/2 square units12. 125/2 square units

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Frequently Asked Questions

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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.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 12 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.