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 6x^1 from x = 0 to x = 2.
6 · 1 · 0 · 2 · Definite power-rule integr…
2. Evaluate the definite integral of 28x^3 from x = 0 to x = 1.
28 · 3 · 0 · 1 · Definite power-rule integr…
3. Evaluate the definite integral of 8x^3 from x = 0 to x = 4.
8 · 3 · 0 · 4 · Definite power-rule integr…
4. Evaluate the definite integral of 16x^3 from x = 0 to x = 5.
16 · 3 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 2x^1 from x = 0 to x = 6.
2 · 1 · 0 · 6 · Definite power-rule integr…
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 3.
15 · 2 · 0 · 3 · Definite power-rule integr…
7. Evaluate the definite integral of 3x^2 from x = 0 to x = 4.
3 · 2 · 0 · 4 · Definite power-rule integr…
8. Evaluate the definite integral of 15x^2 from x = 0 to x = 1.
15 · 2 · 0 · 1 · Definite power-rule integr…
9. Evaluate the definite integral of 18x^2 from x = 0 to x = 1.
18 · 2 · 0 · 1 · Definite power-rule integr…
10. Evaluate the definite integral of 15x^2 from x = 0 to x = 5.
15 · 2 · 0 · 5 · Definite power-rule integr…
11. Evaluate the definite integral of 12x^2 from x = 0 to x = 3.
12 · 2 · 0 · 3 · Definite power-rule integr…
12. Evaluate the definite integral of 15x^2 from x = 0 to x = 2.
15 · 2 · 0 · 2 · Definite power-rule integr…

12 questions · Seed 43 · 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 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.
2. Evaluate the definite integral of 28x^3 from x = 0 to x = 1.
7
An antiderivative of 28x^3 is 7x^4. Evaluating from 0 to 1 gives 7 × 1^4 = 7.
3. 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.
4. Evaluate the definite integral of 16x^3 from x = 0 to x = 5.
2500
An antiderivative of 16x^3 is 4x^4. Evaluating from 0 to 5 gives 4 × 5^4 = 2500.
5. Evaluate the definite integral of 2x^1 from x = 0 to x = 6.
36
An antiderivative of 2x^1 is 1x^2. Evaluating from 0 to 6 gives 1 × 6^2 = 36.
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 3.
135
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 3 gives 5 × 3^3 = 135.
7. Evaluate the definite integral of 3x^2 from x = 0 to x = 4.
64
An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 4 gives 1 × 4^3 = 64.
8. 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.
9. 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.
10. 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.
11. Evaluate the definite integral of 12x^2 from x = 0 to x = 3.
108
An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 3 gives 4 × 3^3 = 108.
12. Evaluate the definite integral of 15x^2 from x = 0 to x = 2.
40
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 2 gives 5 × 2^3 = 40.

12 questions · Seed 43 · 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 6x^1 from x = 0 to x = 2.
6 · 1 · 0 · 2 · Definite power-rule integr…
2. Evaluate the definite integral of 28x^3 from x = 0 to x = 1.
28 · 3 · 0 · 1 · Definite power-rule integr…
3. Evaluate the definite integral of 8x^3 from x = 0 to x = 4.
8 · 3 · 0 · 4 · Definite power-rule integr…
4. Evaluate the definite integral of 16x^3 from x = 0 to x = 5.
16 · 3 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 2x^1 from x = 0 to x = 6.
2 · 1 · 0 · 6 · Definite power-rule integr…
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 3.
15 · 2 · 0 · 3 · Definite power-rule integr…
7. Evaluate the definite integral of 3x^2 from x = 0 to x = 4.
3 · 2 · 0 · 4 · Definite power-rule integr…
8. Evaluate the definite integral of 15x^2 from x = 0 to x = 1.
15 · 2 · 0 · 1 · Definite power-rule integr…
9. Evaluate the definite integral of 18x^2 from x = 0 to x = 1.
18 · 2 · 0 · 1 · Definite power-rule integr…
10. Evaluate the definite integral of 15x^2 from x = 0 to x = 5.
15 · 2 · 0 · 5 · Definite power-rule integr…
11. Evaluate the definite integral of 12x^2 from x = 0 to x = 3.
12 · 2 · 0 · 3 · Definite power-rule integr…
12. Evaluate the definite integral of 15x^2 from x = 0 to x = 2.
15 · 2 · 0 · 2 · Definite power-rule integr…

12 questions · Seed 43 · 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 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.
2. Evaluate the definite integral of 28x^3 from x = 0 to x = 1.
7
An antiderivative of 28x^3 is 7x^4. Evaluating from 0 to 1 gives 7 × 1^4 = 7.
3. 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.
4. Evaluate the definite integral of 16x^3 from x = 0 to x = 5.
2500
An antiderivative of 16x^3 is 4x^4. Evaluating from 0 to 5 gives 4 × 5^4 = 2500.
5. Evaluate the definite integral of 2x^1 from x = 0 to x = 6.
36
An antiderivative of 2x^1 is 1x^2. Evaluating from 0 to 6 gives 1 × 6^2 = 36.
6. Evaluate the definite integral of 15x^2 from x = 0 to x = 3.
135
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 3 gives 5 × 3^3 = 135.
7. Evaluate the definite integral of 3x^2 from x = 0 to x = 4.
64
An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 4 gives 1 × 4^3 = 64.
8. 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.
9. 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.
10. 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.
11. Evaluate the definite integral of 12x^2 from x = 0 to x = 3.
108
An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 3 gives 4 × 3^3 = 108.
12. Evaluate the definite integral of 15x^2 from x = 0 to x = 2.
40
An antiderivative of 15x^2 is 5x^3. Evaluating from 0 to 2 gives 5 × 2^3 = 40.

12 questions · Seed 43 · Age guidance, not curriculum certification