Mathematics · Grades 12–12
Definite integrals of powers
Use an antiderivative at the upper bound minus its value at the lower bound.
The key idea
Use an antiderivative at the upper bound minus its value at the lower bound.
∫₀ᵇ axⁿ dx = abⁿ⁺¹/(n + 1), n ≠ −1
Worked examples
Evaluate the definite integral of 18x^2 from x = 0 to x = 4.
[6x^3]₀^4 = 384
384
Evaluate the definite integral of 24x^2 from x = 0 to x = 7.
[8x^3]₀^7 = 2744
2744
Try it yourself
Evaluate the definite integral of 21x^2 from x = 0 to x = 1.
Evaluate the definite integral of 20x^3 from x = 0 to x = 1.
Check your understanding
Answers and marking notes
- 7
[7x^3]₀^1 = 7
- 5
[5x^4]₀^1 = 5
Further reading and review references
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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.