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Grade 12Common Core (CCSS) · Math: algebra

Math · Grade 12

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Definite integrals · Grade 12

Name: ____________________

Worked example

  1. Find an antiderivative: axⁿ becomes a·xⁿ⁺¹/(n + 1).
  2. Calculate F(upper limit) − F(0).
  3. Example: ∫₀² 2x dx = [x²] = 4 − 0 = 4.
Example: how to solve it
1.

Calculate the integral: ∫₀² (4x) dx =

2.

Calculate the integral: ∫₀² (6x + 4) dx =

3.

Calculate the integral: ∫₀⁴ (2x + 1) dx =

4.

Calculate the integral: ∫₀¹ (6x) dx =

5.

Calculate the integral: ∫₀⁴ (4x + 3) dx =

6.

Calculate the integral: ∫₀² (6x + 2) dx =

7.

Calculate the integral: ∫₀⁴ (2x + 2) dx =

8.

Calculate the integral: ∫₀² (2x + 4) dx =

9.

Calculate the integral: ∫₀³ (4x) dx =

10.

Calculate the integral: ∫₀⁴ (8x + 6) dx =

11.

Calculate the integral: ∫₀¹ (4x + 1) dx =

12.

Calculate the integral: ∫₀³ (4x + 4) dx =

13.

Calculate the integral: ∫₀³ (2x + 3) dx =

14.

Calculate the integral: ∫₀² (6x + 5) dx =

15.

Calculate the integral: ∫₀² (6x) dx =

16.

Calculate the integral: ∫₀³ (4x + 6) dx =

17.

Calculate the integral: ∫₀⁴ (4x + 2) dx =

18.

Calculate the integral: ∫₀⁴ (8x + 3) dx =

19.

Calculate the integral: ∫₀⁴ (2x + 5) dx =

20.

Calculate the integral: ∫₀⁴ (6x + 2) dx =

Answer key

  1. 1. 8
  2. 2. 20
  3. 3. 20
  4. 4. 3
  5. 5. 44
  6. 6. 16
  7. 7. 24
  8. 8. 12
  9. 9. 18
  10. 10. 88
  11. 11. 3
  12. 12. 30
  13. 13. 18
  14. 14. 22
  15. 15. 12
  16. 16. 36
  17. 17. 40
  18. 18. 76
  19. 19. 36
  20. 20. 56

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Area
Algebra
Exercise type
Definite integrals
Grade
12 (ages 17–18)
Difficulty
Easy
Number of tasks
20
Task format
Calculations
Paper size
US Letter
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Practise antiderivatives and definite integrals of polynomials.

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About this generator

Each integral is F(b) − F(0) with whole-number answers. The answer key is calculated by the website. No sign-up needed.

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