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