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. Evaluate the definite integral of 8x^1 from x = 0 to x = 1.
8 · 1 · 0 · 1 · Definite power-rule integr…
2. Evaluate the definite integral of 12x^1 from x = 0 to x = 1.
12 · 1 · 0 · 1 · Definite power-rule integr…
3. Evaluate the definite integral of 2x^1 from x = 0 to x = 2.
2 · 1 · 0 · 2 · Definite power-rule integr…
4. Evaluate the definite integral of 12x^2 from x = 0 to x = 5.
12 · 2 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 1.
16 · 3 · 0 · 1 · Definite power-rule integr…
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 6.
15 · 2 · 0 · 6 · Definite power-rule integr…
7. Evaluate the definite integral of 15x^2 from x = 0 to x = 5.
15 · 2 · 0 · 5 · Definite power-rule integr…
8. Evaluate the definite integral of 6x^2 from x = 0 to x = 3.
6 · 2 · 0 · 3 · Definite power-rule integr…
9. Evaluate the definite integral of 24x^3 from x = 0 to x = 5.
24 · 3 · 0 · 5 · Definite power-rule integr…
10. Evaluate the definite integral of 6x^1 from x = 0 to x = 2.
6 · 1 · 0 · 2 · Definite power-rule integr…
11. Evaluate the definite integral of 15x^2 from x = 0 to x = 1.
15 · 2 · 0 · 1 · Definite power-rule integr…
12. Evaluate the definite integral of 6x^1 from x = 0 to x = 4.
6 · 1 · 0 · 4 · Definite power-rule integr…

12 questions · Seed 53 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 16-18

Definite power-rule integrals

Answers and reasoning. Review before teaching.

1. Evaluate the definite integral of 8x^1 from x = 0 to x = 1.
4
An antiderivative of 8x^1 is 4x^2. Evaluating from 0 to 1 gives 4 × 1^2 = 4.
2. Evaluate the definite integral of 12x^1 from x = 0 to x = 1.
6
An antiderivative of 12x^1 is 6x^2. Evaluating from 0 to 1 gives 6 × 1^2 = 6.
3. Evaluate the definite integral of 2x^1 from x = 0 to x = 2.
4
An antiderivative of 2x^1 is 1x^2. Evaluating from 0 to 2 gives 1 × 2^2 = 4.
4. Evaluate the definite integral of 12x^2 from x = 0 to x = 5.
500
An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 5 gives 4 × 5^3 = 500.
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 1.
4
An antiderivative of 16x^3 is 4x^4. Evaluating from 0 to 1 gives 4 × 1^4 = 4.
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 6.
1080
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 6 gives 5 × 6^3 = 1080.
7. Evaluate the definite integral of 15x^2 from x = 0 to x = 5.
625
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 5 gives 5 × 5^3 = 625.
8. Evaluate the definite integral of 6x^2 from x = 0 to x = 3.
54
An antiderivative of 6x^2 is 2x^3. Evaluating from 0 to 3 gives 2 × 3^3 = 54.
9. Evaluate the definite integral of 24x^3 from x = 0 to x = 5.
3750
An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 5 gives 6 × 5^4 = 3750.
10. 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.
11. Evaluate the definite integral of 15x^2 from x = 0 to x = 1.
5
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 1 gives 5 × 1^3 = 5.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Definite power-rule integrals

Take your time. Show your thinking.

1. Evaluate the definite integral of 8x^1 from x = 0 to x = 1.
8 · 1 · 0 · 1 · Definite power-rule integr…
2. Evaluate the definite integral of 12x^1 from x = 0 to x = 1.
12 · 1 · 0 · 1 · Definite power-rule integr…
3. Evaluate the definite integral of 2x^1 from x = 0 to x = 2.
2 · 1 · 0 · 2 · Definite power-rule integr…
4. Evaluate the definite integral of 12x^2 from x = 0 to x = 5.
12 · 2 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 1.
16 · 3 · 0 · 1 · Definite power-rule integr…
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 6.
15 · 2 · 0 · 6 · Definite power-rule integr…
7. Evaluate the definite integral of 15x^2 from x = 0 to x = 5.
15 · 2 · 0 · 5 · Definite power-rule integr…
8. Evaluate the definite integral of 6x^2 from x = 0 to x = 3.
6 · 2 · 0 · 3 · Definite power-rule integr…
9. Evaluate the definite integral of 24x^3 from x = 0 to x = 5.
24 · 3 · 0 · 5 · Definite power-rule integr…
10. Evaluate the definite integral of 6x^1 from x = 0 to x = 2.
6 · 1 · 0 · 2 · Definite power-rule integr…
11. Evaluate the definite integral of 15x^2 from x = 0 to x = 1.
15 · 2 · 0 · 1 · Definite power-rule integr…
12. Evaluate the definite integral of 6x^1 from x = 0 to x = 4.
6 · 1 · 0 · 4 · Definite power-rule integr…

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Definite power-rule integrals

Answers and reasoning. Review before teaching.

1. Evaluate the definite integral of 8x^1 from x = 0 to x = 1.
4
An antiderivative of 8x^1 is 4x^2. Evaluating from 0 to 1 gives 4 × 1^2 = 4.
2. Evaluate the definite integral of 12x^1 from x = 0 to x = 1.
6
An antiderivative of 12x^1 is 6x^2. Evaluating from 0 to 1 gives 6 × 1^2 = 6.
3. Evaluate the definite integral of 2x^1 from x = 0 to x = 2.
4
An antiderivative of 2x^1 is 1x^2. Evaluating from 0 to 2 gives 1 × 2^2 = 4.
4. Evaluate the definite integral of 12x^2 from x = 0 to x = 5.
500
An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 5 gives 4 × 5^3 = 500.
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 1.
4
An antiderivative of 16x^3 is 4x^4. Evaluating from 0 to 1 gives 4 × 1^4 = 4.
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 6.
1080
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 6 gives 5 × 6^3 = 1080.
7. Evaluate the definite integral of 15x^2 from x = 0 to x = 5.
625
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 5 gives 5 × 5^3 = 625.
8. Evaluate the definite integral of 6x^2 from x = 0 to x = 3.
54
An antiderivative of 6x^2 is 2x^3. Evaluating from 0 to 3 gives 2 × 3^3 = 54.
9. Evaluate the definite integral of 24x^3 from x = 0 to x = 5.
3750
An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 5 gives 6 × 5^4 = 3750.
10. 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.
11. Evaluate the definite integral of 15x^2 from x = 0 to x = 1.
5
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 1 gives 5 × 1^3 = 5.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification