Year 12 Integration (Polynomials) Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (4x − 1) dx
Answer: 2x2 − x + C
- ∫ 4x dx = 2x2
- ∫ −1 dx = −x
- Don't forget the constant of integration, C
2.Find ∫ (8x + 2) dx
Answer: 4x2 + 2x + C
- ∫ 8x dx = 4x2
- ∫ 2 dx = 2x
- Don't forget the constant of integration, C
3.Find ∫ (−9x2 + 2) dx
Answer: −3x3 + 2x + C
- ∫ −9x2 dx = −3x3
- ∫ 2 dx = 2x
- Don't forget the constant of integration, C
4.Find ∫ (−15x4 + 12x2) dx
Answer: −3x5 + 4x3 + C
- ∫ −15x4 dx = −3x5
- ∫ 12x2 dx = 4x3
- Don't forget the constant of integration, C
5.Find ∫ (−12x3 + 3x2) dx
Answer: −3x4 + x3 + C
- ∫ −12x3 dx = −3x4
- ∫ 3x2 dx = x3
- Don't forget the constant of integration, C
6.Find ∫ (−12x3 − 3x2) dx
Answer: −3x4 − x3 + C
- ∫ −12x3 dx = −3x4
- ∫ −3x2 dx = −x3
- Don't forget the constant of integration, C
7.Find ∫ (−15x4 + 16x3) dx
Answer: −3x5 + 4x4 + C
- ∫ −15x4 dx = −3x5
- ∫ 16x3 dx = 4x4
- Don't forget the constant of integration, C
8.Find ∫ (−15x4 + 12x3) dx
Answer: −3x5 + 3x4 + C
- ∫ −15x4 dx = −3x5
- ∫ 12x3 dx = 3x4
- 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 ∫ (20x4 − 2) dx
Answer: 4x5 − 2x + C
- ∫ 20x4 dx = 4x5
- ∫ −2 dx = −2x
- Don't forget the constant of integration, C
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