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 9x^2 from x = 0 to x = 6.
9 · 2 · 0 · 6 · Definite power-rule integr…
2. Evaluate the definite integral of 18x^2 from x = 0 to x = 3.
18 · 2 · 0 · 3 · Definite power-rule integr…
3. Evaluate the definite integral of 15x^2 from x = 0 to x = 3.
15 · 2 · 0 · 3 · Definite power-rule integr…
4. Evaluate the definite integral of 8x^3 from x = 0 to x = 3.
8 · 3 · 0 · 3 · Definite power-rule integr…
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 4.
16 · 3 · 0 · 4 · Definite power-rule integr…
6. Evaluate the definite integral of 12x^2 from x = 0 to x = 5.
12 · 2 · 0 · 5 · Definite power-rule integr…
7. Evaluate the definite integral of 2x^1 from x = 0 to x = 4.
2 · 1 · 0 · 4 · Definite power-rule integr…
8. Evaluate the definite integral of 12x^2 from x = 0 to x = 4.
12 · 2 · 0 · 4 · Definite power-rule integr…
9. Evaluate the definite integral of 12x^2 from x = 0 to x = 1.
12 · 2 · 0 · 1 · Definite power-rule integr…
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 5.
12 · 3 · 0 · 5 · Definite power-rule integr…
11. Evaluate the definite integral of 24x^3 from x = 0 to x = 6.
24 · 3 · 0 · 6 · Definite power-rule integr…
12. Evaluate the definite integral of 12x^1 from x = 0 to x = 3.
12 · 1 · 0 · 3 · Definite power-rule integr…

12 questions · Seed 44 · 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 9x^2 from x = 0 to x = 6.
648
An antiderivative of 9x^2 is 3x^3. Evaluating from 0 to 6 gives 3 × 6^3 = 648.
2. 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.
3. 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.
4. Evaluate the definite integral of 8x^3 from x = 0 to x = 3.
162
An antiderivative of 8x^3 is 2x^4. Evaluating from 0 to 3 gives 2 × 3^4 = 162.
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 4.
1024
An antiderivative of 16x^3 is 4x^4. Evaluating from 0 to 4 gives 4 × 4^4 = 1024.
6. 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.
7. Evaluate the definite integral of 2x^1 from x = 0 to x = 4.
16
An antiderivative of 2x^1 is 1x^2. Evaluating from 0 to 4 gives 1 × 4^2 = 16.
8. Evaluate the definite integral of 12x^2 from x = 0 to x = 4.
256
An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 4 gives 4 × 4^3 = 256.
9. 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.
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 5.
1875
An antiderivative of 12x^3 is 3x^4. Evaluating from 0 to 5 gives 3 × 5^4 = 1875.
11. 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.
12. 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.

12 questions · Seed 44 · 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 9x^2 from x = 0 to x = 6.
9 · 2 · 0 · 6 · Definite power-rule integr…
2. Evaluate the definite integral of 18x^2 from x = 0 to x = 3.
18 · 2 · 0 · 3 · Definite power-rule integr…
3. Evaluate the definite integral of 15x^2 from x = 0 to x = 3.
15 · 2 · 0 · 3 · Definite power-rule integr…
4. Evaluate the definite integral of 8x^3 from x = 0 to x = 3.
8 · 3 · 0 · 3 · Definite power-rule integr…
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 4.
16 · 3 · 0 · 4 · Definite power-rule integr…
6. Evaluate the definite integral of 12x^2 from x = 0 to x = 5.
12 · 2 · 0 · 5 · Definite power-rule integr…
7. Evaluate the definite integral of 2x^1 from x = 0 to x = 4.
2 · 1 · 0 · 4 · Definite power-rule integr…
8. Evaluate the definite integral of 12x^2 from x = 0 to x = 4.
12 · 2 · 0 · 4 · Definite power-rule integr…
9. Evaluate the definite integral of 12x^2 from x = 0 to x = 1.
12 · 2 · 0 · 1 · Definite power-rule integr…
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 5.
12 · 3 · 0 · 5 · Definite power-rule integr…
11. Evaluate the definite integral of 24x^3 from x = 0 to x = 6.
24 · 3 · 0 · 6 · Definite power-rule integr…
12. Evaluate the definite integral of 12x^1 from x = 0 to x = 3.
12 · 1 · 0 · 3 · Definite power-rule integr…

12 questions · Seed 44 · 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 9x^2 from x = 0 to x = 6.
648
An antiderivative of 9x^2 is 3x^3. Evaluating from 0 to 6 gives 3 × 6^3 = 648.
2. 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.
3. 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.
4. Evaluate the definite integral of 8x^3 from x = 0 to x = 3.
162
An antiderivative of 8x^3 is 2x^4. Evaluating from 0 to 3 gives 2 × 3^4 = 162.
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 4.
1024
An antiderivative of 16x^3 is 4x^4. Evaluating from 0 to 4 gives 4 × 4^4 = 1024.
6. 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.
7. Evaluate the definite integral of 2x^1 from x = 0 to x = 4.
16
An antiderivative of 2x^1 is 1x^2. Evaluating from 0 to 4 gives 1 × 4^2 = 16.
8. Evaluate the definite integral of 12x^2 from x = 0 to x = 4.
256
An antiderivative of 12x^2 is 4x^3. Evaluating from 0 to 4 gives 4 × 4^3 = 256.
9. 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.
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 5.
1875
An antiderivative of 12x^3 is 3x^4. Evaluating from 0 to 5 gives 3 × 5^4 = 1875.
11. 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.
12. 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.

12 questions · Seed 44 · Age guidance, not curriculum certification