Year 11 Integration (Polynomials) Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · CalculusYear 11 Integration (Polynomials) Worksheet — Level 1 — Practice Set 4 — Answers
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (9x2 + 3) dx
Answer: 3x3 + 3x + C
- ∫ 9x2 dx = 3x3
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
2.Find ∫ (12x3 + 4x) dx
Answer: 3x4 + 2x2 + C
- ∫ 12x3 dx = 3x4
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
3.Find ∫ (9x2 + 8x) dx
Answer: 3x3 + 4x2 + C
- ∫ 9x2 dx = 3x3
- ∫ 8x dx = 4x2
- Don't forget the constant of integration, C
4.Find ∫ (−8x3 + 9x2) dx
Answer: −2x4 + 3x3 + C
- ∫ −8x3 dx = −2x4
- ∫ 9x2 dx = 3x3
- Don't forget the constant of integration, C
5.Find ∫ (3x2 + 4x) dx
Answer: x3 + 2x2 + C
- ∫ 3x2 dx = x3
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
6.Find ∫ (20x4 + 16x3) dx
Answer: 4x5 + 4x4 + C
- ∫ 20x4 dx = 4x5
- ∫ 16x3 dx = 4x4
- Don't forget the constant of integration, C
7.Find ∫ (12x3 + 1) dx
Answer: 3x4 + x + C
- ∫ 12x3 dx = 3x4
- ∫ 1 dx = x
- Don't forget the constant of integration, C
8.Find ∫ (10x4 + 6x2) dx
Answer: 2x5 + 2x3 + C
- ∫ 10x4 dx = 2x5
- ∫ 6x2 dx = 2x3
- Don't forget the constant of integration, C
9.Find ∫ (−10x4 + 1) dx
Answer: −2x5 + x + C
- ∫ −10x4 dx = −2x5
- ∫ 1 dx = x
- Don't forget the constant of integration, C
10.Find ∫ (15x4 + 12x2) dx
Answer: 3x5 + 4x3 + C
- ∫ 15x4 dx = 3x5
- ∫ 12x2 dx = 4x3
- Don't forget the constant of integration, C
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