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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 3x^2 from x = 0 to x = 2.

    3 · 2 · 0 · 2 · Definite power-rule integr…

  2. 2. Evaluate the definite integral of 8x^3 from x = 0 to x = 4.

    8 · 3 · 0 · 4 · Definite power-rule integr…

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

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

  4. 4. Evaluate the definite integral of 24x^3 from x = 0 to x = 6.

    24 · 3 · 0 · 6 · Definite power-rule integr…

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

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

  6. 6. Evaluate the definite integral of 14x^1 from x = 0 to x = 1.

    14 · 1 · 0 · 1 · Definite power-rule integr…

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

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

  8. 8. Evaluate the definite integral of 9x^2 from x = 0 to x = 1.

    9 · 2 · 0 · 1 · Definite power-rule integr…

  9. 9. Evaluate the definite integral of 4x^3 from x = 0 to x = 2.

    4 · 3 · 0 · 2 · Definite power-rule integr…

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

    12 · 3 · 0 · 3 · Definite power-rule integr…

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

    6 · 1 · 0 · 2 · Definite power-rule integr…

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

    9 · 2 · 0 · 2 · Definite power-rule integr…
12 questions · Seed 104731 · 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 3x^2 from x = 0 to x = 2.

    8

    An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 2 gives 1 × 2^3 = 8.

  2. 2. Evaluate the definite integral of 8x^3 from x = 0 to x = 4.

    512

    An antiderivative of 8x^3 is 2x^4. Evaluating from 0 to 4 gives 2 × 4^4 = 512.

  3. 3. 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.

  4. 4. Evaluate the definite integral of 24x^3 from x = 0 to x = 6.

    7776

    An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 6 gives 6 × 6^4 = 7776.

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

    72

    An antiderivative of 4x^1 is 2x^2. Evaluating from 0 to 6 gives 2 × 6^2 = 72.

  6. 6. Evaluate the definite integral of 14x^1 from x = 0 to x = 1.

    7

    An antiderivative of 14x^1 is 7x^2. Evaluating from 0 to 1 gives 7 × 1^2 = 7.

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

    56

    An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 2 gives 7 × 2^3 = 56.

  8. 8. Evaluate the definite integral of 9x^2 from x = 0 to x = 1.

    3

    An antiderivative of 9x^2 is 3x^3. Evaluating from 0 to 1 gives 3 × 1^3 = 3.

  9. 9. Evaluate the definite integral of 4x^3 from x = 0 to x = 2.

    16

    An antiderivative of 4x^3 is 1x^4. Evaluating from 0 to 2 gives 1 × 2^4 = 16.

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

    243

    An antiderivative of 12x^3 is 3x^4. Evaluating from 0 to 3 gives 3 × 3^4 = 243.

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

    12

    An antiderivative of 6x^1 is 3x^2. Evaluating from 0 to 2 gives 3 × 2^2 = 12.

  12. 12. 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.

12 questions · Seed 104731 · 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 3x^2 from x = 0 to x = 2.

    3 · 2 · 0 · 2 · Definite power-rule integr…

  2. 2. Evaluate the definite integral of 8x^3 from x = 0 to x = 4.

    8 · 3 · 0 · 4 · Definite power-rule integr…

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

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

  4. 4. Evaluate the definite integral of 24x^3 from x = 0 to x = 6.

    24 · 3 · 0 · 6 · Definite power-rule integr…

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

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

  6. 6. Evaluate the definite integral of 14x^1 from x = 0 to x = 1.

    14 · 1 · 0 · 1 · Definite power-rule integr…

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

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

  8. 8. Evaluate the definite integral of 9x^2 from x = 0 to x = 1.

    9 · 2 · 0 · 1 · Definite power-rule integr…

  9. 9. Evaluate the definite integral of 4x^3 from x = 0 to x = 2.

    4 · 3 · 0 · 2 · Definite power-rule integr…

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

    12 · 3 · 0 · 3 · Definite power-rule integr…

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

    6 · 1 · 0 · 2 · Definite power-rule integr…

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

    9 · 2 · 0 · 2 · Definite power-rule integr…
12 questions · Seed 104731 · 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 3x^2 from x = 0 to x = 2.

    8

    An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 2 gives 1 × 2^3 = 8.

  2. 2. Evaluate the definite integral of 8x^3 from x = 0 to x = 4.

    512

    An antiderivative of 8x^3 is 2x^4. Evaluating from 0 to 4 gives 2 × 4^4 = 512.

  3. 3. 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.

  4. 4. Evaluate the definite integral of 24x^3 from x = 0 to x = 6.

    7776

    An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 6 gives 6 × 6^4 = 7776.

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

    72

    An antiderivative of 4x^1 is 2x^2. Evaluating from 0 to 6 gives 2 × 6^2 = 72.

  6. 6. Evaluate the definite integral of 14x^1 from x = 0 to x = 1.

    7

    An antiderivative of 14x^1 is 7x^2. Evaluating from 0 to 1 gives 7 × 1^2 = 7.

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

    56

    An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 2 gives 7 × 2^3 = 56.

  8. 8. Evaluate the definite integral of 9x^2 from x = 0 to x = 1.

    3

    An antiderivative of 9x^2 is 3x^3. Evaluating from 0 to 1 gives 3 × 1^3 = 3.

  9. 9. Evaluate the definite integral of 4x^3 from x = 0 to x = 2.

    16

    An antiderivative of 4x^3 is 1x^4. Evaluating from 0 to 2 gives 1 × 2^4 = 16.

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

    243

    An antiderivative of 12x^3 is 3x^4. Evaluating from 0 to 3 gives 3 × 3^4 = 243.

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

    12

    An antiderivative of 6x^1 is 3x^2. Evaluating from 0 to 2 gives 3 × 2^2 = 12.

  12. 12. 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.

12 questions · Seed 104731 · Age guidance, not curriculum certification