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 12x^1 from x = 0 to x = 6.
12 · 1 · 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 8x^1 from x = 0 to x = 4.
8 · 1 · 0 · 4 · Definite power-rule integr…
4. Evaluate the definite integral of 14x^1 from x = 0 to x = 5.
14 · 1 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 5.
16 · 3 · 0 · 5 · Definite power-rule integr…
6. Evaluate the definite integral of 10x^1 from x = 0 to x = 2.
10 · 1 · 0 · 2 · Definite power-rule integr…
7. Evaluate the definite integral of 3x^2 from x = 0 to x = 5.
3 · 2 · 0 · 5 · Definite power-rule integr…
8. Evaluate the definite integral of 28x^3 from x = 0 to x = 6.
28 · 3 · 0 · 6 · Definite power-rule integr…
9. Evaluate the definite integral of 2x^1 from x = 0 to x = 6.
2 · 1 · 0 · 6 · 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 4x^3 from x = 0 to x = 2.
4 · 3 · 0 · 2 · Definite power-rule integr…
12. Evaluate the definite integral of 21x^2 from x = 0 to x = 4.
21 · 2 · 0 · 4 · Definite power-rule integr…

12 questions · Seed 47 · 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 12x^1 from x = 0 to x = 6.
216
An antiderivative of 12x^1 is 6x^2. Evaluating from 0 to 6 gives 6 × 6^2 = 216.
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 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.
4. Evaluate the definite integral of 14x^1 from x = 0 to x = 5.
175
An antiderivative of 14x^1 is 7x^2. Evaluating from 0 to 5 gives 7 × 5^2 = 175.
5. 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.
6. Evaluate the definite integral of 10x^1 from x = 0 to x = 2.
20
An antiderivative of 10x^1 is 5x^2. Evaluating from 0 to 2 gives 5 × 2^2 = 20.
7. 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.
8. Evaluate the definite integral of 28x^3 from x = 0 to x = 6.
9072
An antiderivative of 28x^3 is 7x^4. Evaluating from 0 to 6 gives 7 × 6^4 = 9072.
9. 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.
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 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. Evaluate the definite integral of 21x^2 from x = 0 to x = 4.
448
An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 4 gives 7 × 4^3 = 448.

12 questions · Seed 47 · 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 12x^1 from x = 0 to x = 6.
12 · 1 · 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 8x^1 from x = 0 to x = 4.
8 · 1 · 0 · 4 · Definite power-rule integr…
4. Evaluate the definite integral of 14x^1 from x = 0 to x = 5.
14 · 1 · 0 · 5 · Definite power-rule integr…
5. Evaluate the definite integral of 16x^3 from x = 0 to x = 5.
16 · 3 · 0 · 5 · Definite power-rule integr…
6. Evaluate the definite integral of 10x^1 from x = 0 to x = 2.
10 · 1 · 0 · 2 · Definite power-rule integr…
7. Evaluate the definite integral of 3x^2 from x = 0 to x = 5.
3 · 2 · 0 · 5 · Definite power-rule integr…
8. Evaluate the definite integral of 28x^3 from x = 0 to x = 6.
28 · 3 · 0 · 6 · Definite power-rule integr…
9. Evaluate the definite integral of 2x^1 from x = 0 to x = 6.
2 · 1 · 0 · 6 · 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 4x^3 from x = 0 to x = 2.
4 · 3 · 0 · 2 · Definite power-rule integr…
12. Evaluate the definite integral of 21x^2 from x = 0 to x = 4.
21 · 2 · 0 · 4 · Definite power-rule integr…

12 questions · Seed 47 · 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 12x^1 from x = 0 to x = 6.
216
An antiderivative of 12x^1 is 6x^2. Evaluating from 0 to 6 gives 6 × 6^2 = 216.
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 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.
4. Evaluate the definite integral of 14x^1 from x = 0 to x = 5.
175
An antiderivative of 14x^1 is 7x^2. Evaluating from 0 to 5 gives 7 × 5^2 = 175.
5. 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.
6. Evaluate the definite integral of 10x^1 from x = 0 to x = 2.
20
An antiderivative of 10x^1 is 5x^2. Evaluating from 0 to 2 gives 5 × 2^2 = 20.
7. 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.
8. Evaluate the definite integral of 28x^3 from x = 0 to x = 6.
9072
An antiderivative of 28x^3 is 7x^4. Evaluating from 0 to 6 gives 7 × 6^4 = 9072.
9. 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.
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 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. Evaluate the definite integral of 21x^2 from x = 0 to x = 4.
448
An antiderivative of 21x^2 is 7x^3. Evaluating from 0 to 4 gives 7 × 4^3 = 448.

12 questions · Seed 47 · Age guidance, not curriculum certification