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 + 4x) dx
Answer: x5 + 2x2 + C
- ∫ 5x4 dx = x5
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
2.Find ∫ (5x4 + 12x2) dx
Answer: x5 + 4x3 + C
- ∫ 5x4 dx = x5
- ∫ 12x2 dx = 4x3
- Don't forget the constant of integration, C
3.Find ∫ (−12x3 + 9x2) dx
Answer: −3x4 + 3x3 + C
- ∫ −12x3 dx = −3x4
- ∫ 9x2 dx = 3x3
- Don't forget the constant of integration, C
4.Find ∫ (−4x3 + 9x2) dx
Answer: −x4 + 3x3 + C
- ∫ −4x3 dx = −x4
- ∫ 9x2 dx = 3x3
- Don't forget the constant of integration, C
5.Find ∫ (4x3 + 2) dx
Answer: x4 + 2x + C
- ∫ 4x3 dx = x4
- ∫ 2 dx = 2x
- Don't forget the constant of integration, C
6.Find ∫ (10x4 + 8x) dx
Answer: 2x5 + 4x2 + C
- ∫ 10x4 dx = 2x5
- ∫ 8x dx = 4x2
- Don't forget the constant of integration, C
7.Find ∫ (−15x4 + 4x3) dx
Answer: −3x5 + x4 + C
- ∫ −15x4 dx = −3x5
- ∫ 4x3 dx = x4
- Don't forget the constant of integration, C
8.Find ∫ (3x2 − 2x) dx
Answer: x3 − x2 + C
- ∫ 3x2 dx = x3
- ∫ −2x dx = −x2
- Don't forget the constant of integration, C
9.Find ∫ (2x + 3) dx
Answer: x2 + 3x + C
- ∫ 2x dx = x2
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
10.Find ∫ (4x + 3) dx
Answer: 2x2 + 3x + C
- ∫ 4x dx = 2x2
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
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