12th Grade Integration (Polynomials) Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the 12th Grade calculus worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Calculus12th Grade Integration (Polynomials) Worksheet — Level 1 — Practice Set 4 — Answers
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (16x3 + 9x2) dx
Answer: 4x4 + 3x3 + C
- ∫ 16x3 dx = 4x4
- ∫ 9x2 dx = 3x3
- Don't forget the constant of integration, C
2.Find ∫ (3x2 − 1) dx
Answer: x3 − x + C
- ∫ 3x2 dx = x3
- ∫ −1 dx = −x
- Don't forget the constant of integration, C
3.Find ∫ (12x3 + 3) dx
Answer: 3x4 + 3x + C
- ∫ 12x3 dx = 3x4
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
4.Find ∫ (4x3 + 4x) dx
Answer: x4 + 2x2 + C
- ∫ 4x3 dx = x4
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
5.Find ∫ (−6x2 + 2x) dx
Answer: −2x3 + x2 + C
- ∫ −6x2 dx = −2x3
- ∫ 2x dx = x2
- Don't forget the constant of integration, C
6.Find ∫ (6x2 + 4x) dx
Answer: 2x3 + 2x2 + C
- ∫ 6x2 dx = 2x3
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
7.Find ∫ (9x2 + 8x) dx
Answer: 3x3 + 4x2 + C
- ∫ 9x2 dx = 3x3
- ∫ 8x dx = 4x2
- Don't forget the constant of integration, C
8.Find ∫ (20x4 + 4x) dx
Answer: 4x5 + 2x2 + C
- ∫ 20x4 dx = 4x5
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
9.Find ∫ (16x3 − 9x2) dx
Answer: 4x4 − 3x3 + C
- ∫ 16x3 dx = 4x4
- ∫ −9x2 dx = −3x3
- Don't forget the constant of integration, C
10.Find ∫ (5x4 − 8x3) dx
Answer: x5 − 2x4 + C
- ∫ 5x4 dx = x5
- ∫ −8x3 dx = −2x4
- 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.