Year 13 Integration (Polynomials) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 13 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · CalculusYear 13 Integration (Polynomials) Worksheet — Level 1 — Answers
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (4x3 + 3) dx
Answer: x4 + 3x + C
- ∫ 4x3 dx = x4
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
2.Find ∫ (−9x2 + 2x) dx
Answer: −3x3 + x2 + C
- ∫ −9x2 dx = −3x3
- ∫ 2x dx = x2
- Don't forget the constant of integration, C
3.Find ∫ (−5x4 + 9x2) dx
Answer: −x5 + 3x3 + C
- ∫ −5x4 dx = −x5
- ∫ 9x2 dx = 3x3
- Don't forget the constant of integration, C
4.Find ∫ (8x3 − 2x) dx
Answer: 2x4 − x2 + C
- ∫ 8x3 dx = 2x4
- ∫ −2x dx = −x2
- Don't forget the constant of integration, C
5.Find ∫ (−2x + 3) dx
Answer: −x2 + 3x + C
- ∫ −2x dx = −x2
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
6.Find ∫ (2x + 3) dx
Answer: x2 + 3x + C
- ∫ 2x dx = x2
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
7.Find ∫ (4x3 + 2x) dx
Answer: x4 + x2 + C
- ∫ 4x3 dx = x4
- ∫ 2x dx = x2
- Don't forget the constant of integration, C
8.Find ∫ (6x2 − 6x) dx
Answer: 2x3 − 3x2 + C
- ∫ 6x2 dx = 2x3
- ∫ −6x dx = −3x2
- Don't forget the constant of integration, C
9.Find ∫ (−4x − 3) dx
Answer: −2x2 − 3x + C
- ∫ −4x dx = −2x2
- ∫ −3 dx = −3x
- Don't forget the constant of integration, C
10.Find ∫ (−15x4 − 6x) dx
Answer: −3x5 − 3x2 + C
- ∫ −15x4 dx = −3x5
- ∫ −6x dx = −3x2
- Don't forget the constant of integration, C
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.