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