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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 4x^3 from x = 0 to x = 3.

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

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

    8 · 1 · 0 · 4 · Definite power-rule integr…

  3. 3. Evaluate the definite integral of 24x^3 from x = 0 to x = 2.

    24 · 3 · 0 · 2 · Definite power-rule integr…

  4. 4. Evaluate the definite integral of 28x^3 from x = 0 to x = 2.

    28 · 3 · 0 · 2 · Definite power-rule integr…

  5. 5. Evaluate the definite integral of 12x^1 from x = 0 to x = 3.

    12 · 1 · 0 · 3 · Definite power-rule integr…

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

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

  7. 7. Evaluate the definite integral of 18x^2 from x = 0 to x = 3.

    18 · 2 · 0 · 3 · Definite power-rule integr…

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

    4 · 1 · 0 · 5 · Definite power-rule integr…

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

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

  10. 10. Evaluate the definite integral of 4x^1 from x = 0 to x = 2.

    4 · 1 · 0 · 2 · Definite power-rule integr…

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

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

  12. 12. Evaluate the definite integral of 21x^2 from x = 0 to x = 3.

    21 · 2 · 0 · 3 · Definite power-rule integr…
12 questions · Seed 48 · 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 4x^3 from x = 0 to x = 3.

    81

    An antiderivative of 4x^3 is 1x^4. Evaluating from 0 to 3 gives 1 × 3^4 = 81.

  2. 2. 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.

  3. 3. Evaluate the definite integral of 24x^3 from x = 0 to x = 2.

    96

    An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 2 gives 6 × 2^4 = 96.

  4. 4. Evaluate the definite integral of 28x^3 from x = 0 to x = 2.

    112

    An antiderivative of 28x^3 is 7x^4. Evaluating from 0 to 2 gives 7 × 2^4 = 112.

  5. 5. Evaluate the definite integral of 12x^1 from x = 0 to x = 3.

    54

    An antiderivative of 12x^1 is 6x^2. Evaluating from 0 to 3 gives 6 × 3^2 = 54.

  6. 6. 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.

  7. 7. Evaluate the definite integral of 18x^2 from x = 0 to x = 3.

    162

    An antiderivative of 18x^2 is 6x^3. Evaluating from 0 to 3 gives 6 × 3^3 = 162.

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

    50

    An antiderivative of 4x^1 is 2x^2. Evaluating from 0 to 5 gives 2 × 5^2 = 50.

  9. 9. 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.

  10. 10. Evaluate the definite integral of 4x^1 from x = 0 to x = 2.

    8

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

  11. 11. 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.

  12. 12. Evaluate the definite integral of 21x^2 from x = 0 to x = 3.

    189

    An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 3 gives 7 × 3^3 = 189.

12 questions · Seed 48 · 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 4x^3 from x = 0 to x = 3.

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

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

    8 · 1 · 0 · 4 · Definite power-rule integr…

  3. 3. Evaluate the definite integral of 24x^3 from x = 0 to x = 2.

    24 · 3 · 0 · 2 · Definite power-rule integr…

  4. 4. Evaluate the definite integral of 28x^3 from x = 0 to x = 2.

    28 · 3 · 0 · 2 · Definite power-rule integr…

  5. 5. Evaluate the definite integral of 12x^1 from x = 0 to x = 3.

    12 · 1 · 0 · 3 · Definite power-rule integr…

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

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

  7. 7. Evaluate the definite integral of 18x^2 from x = 0 to x = 3.

    18 · 2 · 0 · 3 · Definite power-rule integr…

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

    4 · 1 · 0 · 5 · Definite power-rule integr…

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

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

  10. 10. Evaluate the definite integral of 4x^1 from x = 0 to x = 2.

    4 · 1 · 0 · 2 · Definite power-rule integr…

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

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

  12. 12. Evaluate the definite integral of 21x^2 from x = 0 to x = 3.

    21 · 2 · 0 · 3 · Definite power-rule integr…
12 questions · Seed 48 · 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 4x^3 from x = 0 to x = 3.

    81

    An antiderivative of 4x^3 is 1x^4. Evaluating from 0 to 3 gives 1 × 3^4 = 81.

  2. 2. 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.

  3. 3. Evaluate the definite integral of 24x^3 from x = 0 to x = 2.

    96

    An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 2 gives 6 × 2^4 = 96.

  4. 4. Evaluate the definite integral of 28x^3 from x = 0 to x = 2.

    112

    An antiderivative of 28x^3 is 7x^4. Evaluating from 0 to 2 gives 7 × 2^4 = 112.

  5. 5. Evaluate the definite integral of 12x^1 from x = 0 to x = 3.

    54

    An antiderivative of 12x^1 is 6x^2. Evaluating from 0 to 3 gives 6 × 3^2 = 54.

  6. 6. 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.

  7. 7. Evaluate the definite integral of 18x^2 from x = 0 to x = 3.

    162

    An antiderivative of 18x^2 is 6x^3. Evaluating from 0 to 3 gives 6 × 3^3 = 162.

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

    50

    An antiderivative of 4x^1 is 2x^2. Evaluating from 0 to 5 gives 2 × 5^2 = 50.

  9. 9. 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.

  10. 10. Evaluate the definite integral of 4x^1 from x = 0 to x = 2.

    8

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

  11. 11. 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.

  12. 12. Evaluate the definite integral of 21x^2 from x = 0 to x = 3.

    189

    An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 3 gives 7 × 3^3 = 189.

12 questions · Seed 48 · Age guidance, not curriculum certification