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MathsAges 16-18

Definite power-rule integrals

Integrate a single power term and evaluate the definite integral between x = 0 and an upper bound. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Definite power-rule integrals

Take your time. Show your thinking.

  1. 1. Evaluate the definite integral of 18x^2 from x = 0 to x = 6.

    18 · 2 · 0 · 6 · Definite power-rule integr…

  2. 2. Evaluate the definite integral of 12x^2 from x = 0 to x = 1.

    12 · 2 · 0 · 1 · Definite power-rule integr…

  3. 3. Evaluate the definite integral of 12x^2 from x = 0 to x = 2.

    12 · 2 · 0 · 2 · Definite power-rule integr…

  4. 4. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.

    20 · 3 · 0 · 4 · Definite power-rule integr…

  5. 5. Evaluate the definite integral of 4x^1 from x = 0 to x = 3.

    4 · 1 · 0 · 3 · Definite power-rule integr…

  6. 6. Evaluate the definite integral of 9x^2 from x = 0 to x = 2.

    9 · 2 · 0 · 2 · Definite power-rule integr…

  7. 7. Evaluate the definite integral of 6x^1 from x = 0 to x = 4.

    6 · 1 · 0 · 4 · Definite power-rule integr…

  8. 8. Evaluate the definite integral of 6x^1 from x = 0 to x = 5.

    6 · 1 · 0 · 5 · Definite power-rule integr…

  9. 9. Evaluate the definite integral of 15x^2 from x = 0 to x = 4.

    15 · 2 · 0 · 4 · Definite power-rule integr…

  10. 10. Evaluate the definite integral of 21x^2 from x = 0 to x = 1.

    21 · 2 · 0 · 1 · Definite power-rule integr…

  11. 11. Evaluate the definite integral of 18x^2 from x = 0 to x = 1.

    18 · 2 · 0 · 1 · Definite power-rule integr…

  12. 12. Evaluate the definite integral of 8x^1 from x = 0 to x = 4.

    8 · 1 · 0 · 4 · Definite power-rule integr…
12 questions · Seed 42 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Definite power-rule integrals

Answers and reasoning. Review before teaching.

  1. 1. Evaluate the definite integral of 18x^2 from x = 0 to x = 6.

    1296

    An antiderivative of 18x^2 is 6x^3. Evaluating from 0 to 6 gives 6 × 6^3 = 1296.

  2. 2. Evaluate the definite integral of 12x^2 from x = 0 to x = 1.

    4

    An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 1 gives 4 × 1^3 = 4.

  3. 3. Evaluate the definite integral of 12x^2 from x = 0 to x = 2.

    32

    An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 2 gives 4 × 2^3 = 32.

  4. 4. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.

    1280

    An antiderivative of 20x^3 is 5x^4. Evaluating from 0 to 4 gives 5 × 4^4 = 1280.

  5. 5. Evaluate the definite integral of 4x^1 from x = 0 to x = 3.

    18

    An antiderivative of 4x^1 is 2x^2. Evaluating from 0 to 3 gives 2 × 3^2 = 18.

  6. 6. Evaluate the definite integral of 9x^2 from x = 0 to x = 2.

    24

    An antiderivative of 9x^2 is 3x^3. Evaluating from 0 to 2 gives 3 × 2^3 = 24.

  7. 7. Evaluate the definite integral of 6x^1 from x = 0 to x = 4.

    48

    An antiderivative of 6x^1 is 3x^2. Evaluating from 0 to 4 gives 3 × 4^2 = 48.

  8. 8. Evaluate the definite integral of 6x^1 from x = 0 to x = 5.

    75

    An antiderivative of 6x^1 is 3x^2. Evaluating from 0 to 5 gives 3 × 5^2 = 75.

  9. 9. Evaluate the definite integral of 15x^2 from x = 0 to x = 4.

    320

    An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 4 gives 5 × 4^3 = 320.

  10. 10. Evaluate the definite integral of 21x^2 from x = 0 to x = 1.

    7

    An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 1 gives 7 × 1^3 = 7.

  11. 11. Evaluate the definite integral of 18x^2 from x = 0 to x = 1.

    6

    An antiderivative of 18x^2 is 6x^3. Evaluating from 0 to 1 gives 6 × 1^3 = 6.

  12. 12. Evaluate the definite integral of 8x^1 from x = 0 to x = 4.

    64

    An antiderivative of 8x^1 is 4x^2. Evaluating from 0 to 4 gives 4 × 4^2 = 64.

12 questions · Seed 42 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Definite power-rule integrals

Take your time. Show your thinking.

  1. 1. Evaluate the definite integral of 18x^2 from x = 0 to x = 6.

    18 · 2 · 0 · 6 · Definite power-rule integr…

  2. 2. Evaluate the definite integral of 12x^2 from x = 0 to x = 1.

    12 · 2 · 0 · 1 · Definite power-rule integr…

  3. 3. Evaluate the definite integral of 12x^2 from x = 0 to x = 2.

    12 · 2 · 0 · 2 · Definite power-rule integr…

  4. 4. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.

    20 · 3 · 0 · 4 · Definite power-rule integr…

  5. 5. Evaluate the definite integral of 4x^1 from x = 0 to x = 3.

    4 · 1 · 0 · 3 · Definite power-rule integr…

  6. 6. Evaluate the definite integral of 9x^2 from x = 0 to x = 2.

    9 · 2 · 0 · 2 · Definite power-rule integr…

  7. 7. Evaluate the definite integral of 6x^1 from x = 0 to x = 4.

    6 · 1 · 0 · 4 · Definite power-rule integr…

  8. 8. Evaluate the definite integral of 6x^1 from x = 0 to x = 5.

    6 · 1 · 0 · 5 · Definite power-rule integr…

  9. 9. Evaluate the definite integral of 15x^2 from x = 0 to x = 4.

    15 · 2 · 0 · 4 · Definite power-rule integr…

  10. 10. Evaluate the definite integral of 21x^2 from x = 0 to x = 1.

    21 · 2 · 0 · 1 · Definite power-rule integr…

  11. 11. Evaluate the definite integral of 18x^2 from x = 0 to x = 1.

    18 · 2 · 0 · 1 · Definite power-rule integr…

  12. 12. Evaluate the definite integral of 8x^1 from x = 0 to x = 4.

    8 · 1 · 0 · 4 · Definite power-rule integr…
12 questions · Seed 42 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Definite power-rule integrals

Answers and reasoning. Review before teaching.

  1. 1. Evaluate the definite integral of 18x^2 from x = 0 to x = 6.

    1296

    An antiderivative of 18x^2 is 6x^3. Evaluating from 0 to 6 gives 6 × 6^3 = 1296.

  2. 2. Evaluate the definite integral of 12x^2 from x = 0 to x = 1.

    4

    An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 1 gives 4 × 1^3 = 4.

  3. 3. Evaluate the definite integral of 12x^2 from x = 0 to x = 2.

    32

    An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 2 gives 4 × 2^3 = 32.

  4. 4. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.

    1280

    An antiderivative of 20x^3 is 5x^4. Evaluating from 0 to 4 gives 5 × 4^4 = 1280.

  5. 5. Evaluate the definite integral of 4x^1 from x = 0 to x = 3.

    18

    An antiderivative of 4x^1 is 2x^2. Evaluating from 0 to 3 gives 2 × 3^2 = 18.

  6. 6. Evaluate the definite integral of 9x^2 from x = 0 to x = 2.

    24

    An antiderivative of 9x^2 is 3x^3. Evaluating from 0 to 2 gives 3 × 2^3 = 24.

  7. 7. Evaluate the definite integral of 6x^1 from x = 0 to x = 4.

    48

    An antiderivative of 6x^1 is 3x^2. Evaluating from 0 to 4 gives 3 × 4^2 = 48.

  8. 8. Evaluate the definite integral of 6x^1 from x = 0 to x = 5.

    75

    An antiderivative of 6x^1 is 3x^2. Evaluating from 0 to 5 gives 3 × 5^2 = 75.

  9. 9. Evaluate the definite integral of 15x^2 from x = 0 to x = 4.

    320

    An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 4 gives 5 × 4^3 = 320.

  10. 10. Evaluate the definite integral of 21x^2 from x = 0 to x = 1.

    7

    An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 1 gives 7 × 1^3 = 7.

  11. 11. Evaluate the definite integral of 18x^2 from x = 0 to x = 1.

    6

    An antiderivative of 18x^2 is 6x^3. Evaluating from 0 to 1 gives 6 × 1^3 = 6.

  12. 12. Evaluate the definite integral of 8x^1 from x = 0 to x = 4.

    64

    An antiderivative of 8x^1 is 4x^2. Evaluating from 0 to 4 gives 4 × 4^2 = 64.

12 questions · Seed 42 · Age guidance, not curriculum certification