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 4x^1 from x = 0 to x = 5.
4 · 1 · 0 · 5 · Definite power-rule integr…
2. Evaluate the definite integral of 3x^2 from x = 0 to x = 6.
3 · 2 · 0 · 6 · Definite power-rule integr…
3. Evaluate the definite integral of 8x^1 from x = 0 to x = 6.
8 · 1 · 0 · 6 · Definite power-rule integr…
4. Evaluate the definite integral of 3x^2 from x = 0 to x = 5.
3 · 2 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 10x^1 from x = 0 to x = 4.
10 · 1 · 0 · 4 · Definite power-rule integr…
6. Evaluate the definite integral of 6x^2 from x = 0 to x = 3.
6 · 2 · 0 · 3 · Definite power-rule integr…
7. Evaluate the definite integral of 28x^3 from x = 0 to x = 2.
28 · 3 · 0 · 2 · Definite power-rule integr…
8. Evaluate the definite integral of 14x^1 from x = 0 to x = 2.
14 · 1 · 0 · 2 · Definite power-rule integr…
9. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.
20 · 3 · 0 · 4 · Definite power-rule integr…
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 4.
12 · 3 · 0 · 4 · Definite power-rule integr…
11. Evaluate the definite integral of 20x^3 from x = 0 to x = 6.
20 · 3 · 0 · 6 · Definite power-rule integr…
12. Evaluate the definite integral of 24x^3 from x = 0 to x = 3.
24 · 3 · 0 · 3 · Definite power-rule integr…

12 questions · Seed 46 · 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 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.
2. Evaluate the definite integral of 3x^2 from x = 0 to x = 6.
216
An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 6 gives 1 × 6^3 = 216.
3. Evaluate the definite integral of 8x^1 from x = 0 to x = 6.
144
An antiderivative of 8x^1 is 4x^2. Evaluating from 0 to 6 gives 4 × 6^2 = 144.
4. Evaluate the definite integral of 3x^2 from x = 0 to x = 5.
125
An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 5 gives 1 × 5^3 = 125.
5. Evaluate the definite integral of 10x^1 from x = 0 to x = 4.
80
An antiderivative of 10x^1 is 5x^2. Evaluating from 0 to 4 gives 5 × 4^2 = 80.
6. 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.
7. 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.
8. Evaluate the definite integral of 14x^1 from x = 0 to x = 2.
28
An antiderivative of 14x^1 is 7x^2. Evaluating from 0 to 2 gives 7 × 2^2 = 28.
9. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.
1280
An antiderivative of 20x^3 is 5x^4. Evaluating from 0 to 4 gives 5 × 4^4 = 1280.
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 4.
768
An antiderivative of 12x^3 is 3x^4. Evaluating from 0 to 4 gives 3 × 4^4 = 768.
11. Evaluate the definite integral of 20x^3 from x = 0 to x = 6.
6480
An antiderivative of 20x^3 is 5x^4. Evaluating from 0 to 6 gives 5 × 6^4 = 6480.
12. Evaluate the definite integral of 24x^3 from x = 0 to x = 3.
486
An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 3 gives 6 × 3^4 = 486.

12 questions · Seed 46 · 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 4x^1 from x = 0 to x = 5.
4 · 1 · 0 · 5 · Definite power-rule integr…
2. Evaluate the definite integral of 3x^2 from x = 0 to x = 6.
3 · 2 · 0 · 6 · Definite power-rule integr…
3. Evaluate the definite integral of 8x^1 from x = 0 to x = 6.
8 · 1 · 0 · 6 · Definite power-rule integr…
4. Evaluate the definite integral of 3x^2 from x = 0 to x = 5.
3 · 2 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 10x^1 from x = 0 to x = 4.
10 · 1 · 0 · 4 · Definite power-rule integr…
6. Evaluate the definite integral of 6x^2 from x = 0 to x = 3.
6 · 2 · 0 · 3 · Definite power-rule integr…
7. Evaluate the definite integral of 28x^3 from x = 0 to x = 2.
28 · 3 · 0 · 2 · Definite power-rule integr…
8. Evaluate the definite integral of 14x^1 from x = 0 to x = 2.
14 · 1 · 0 · 2 · Definite power-rule integr…
9. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.
20 · 3 · 0 · 4 · Definite power-rule integr…
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 4.
12 · 3 · 0 · 4 · Definite power-rule integr…
11. Evaluate the definite integral of 20x^3 from x = 0 to x = 6.
20 · 3 · 0 · 6 · Definite power-rule integr…
12. Evaluate the definite integral of 24x^3 from x = 0 to x = 3.
24 · 3 · 0 · 3 · Definite power-rule integr…

12 questions · Seed 46 · 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 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.
2. Evaluate the definite integral of 3x^2 from x = 0 to x = 6.
216
An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 6 gives 1 × 6^3 = 216.
3. Evaluate the definite integral of 8x^1 from x = 0 to x = 6.
144
An antiderivative of 8x^1 is 4x^2. Evaluating from 0 to 6 gives 4 × 6^2 = 144.
4. Evaluate the definite integral of 3x^2 from x = 0 to x = 5.
125
An antiderivative of 3x^2 is 1x^3. Evaluating from 0 to 5 gives 1 × 5^3 = 125.
5. Evaluate the definite integral of 10x^1 from x = 0 to x = 4.
80
An antiderivative of 10x^1 is 5x^2. Evaluating from 0 to 4 gives 5 × 4^2 = 80.
6. 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.
7. 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.
8. Evaluate the definite integral of 14x^1 from x = 0 to x = 2.
28
An antiderivative of 14x^1 is 7x^2. Evaluating from 0 to 2 gives 7 × 2^2 = 28.
9. Evaluate the definite integral of 20x^3 from x = 0 to x = 4.
1280
An antiderivative of 20x^3 is 5x^4. Evaluating from 0 to 4 gives 5 × 4^4 = 1280.
10. Evaluate the definite integral of 12x^3 from x = 0 to x = 4.
768
An antiderivative of 12x^3 is 3x^4. Evaluating from 0 to 4 gives 3 × 4^4 = 768.
11. Evaluate the definite integral of 20x^3 from x = 0 to x = 6.
6480
An antiderivative of 20x^3 is 5x^4. Evaluating from 0 to 6 gives 5 × 6^4 = 6480.
12. Evaluate the definite integral of 24x^3 from x = 0 to x = 3.
486
An antiderivative of 24x^3 is 6x^4. Evaluating from 0 to 3 gives 6 × 3^4 = 486.

12 questions · Seed 46 · Age guidance, not curriculum certification