Year 13 Integration (Polynomials) Worksheet — Level 1 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 13 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · CalculusYear 13 Integration (Polynomials) Worksheet — Level 1 — Practice Set 2 — Answers
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (2x + 4) dx
Answer: x2 + 4x + C
- ∫ 2x dx = x2
- ∫ 4 dx = 4x
- Don't forget the constant of integration, C
2.Find ∫ (15x4 + 16x3) dx
Answer: 3x5 + 4x4 + C
- ∫ 15x4 dx = 3x5
- ∫ 16x3 dx = 4x4
- Don't forget the constant of integration, C
3.Find ∫ (−3x2 + 1) dx
Answer: −x3 + x + C
- ∫ −3x2 dx = −x3
- ∫ 1 dx = x
- Don't forget the constant of integration, C
4.Find ∫ (20x4 − 4x3) dx
Answer: 4x5 − x4 + C
- ∫ 20x4 dx = 4x5
- ∫ −4x3 dx = −x4
- Don't forget the constant of integration, C
5.Find ∫ (15x4 − 2) dx
Answer: 3x5 − 2x + C
- ∫ 15x4 dx = 3x5
- ∫ −2 dx = −2x
- Don't forget the constant of integration, C
6.Find ∫ (−9x2 + 4) dx
Answer: −3x3 + 4x + C
- ∫ −9x2 dx = −3x3
- ∫ 4 dx = 4x
- Don't forget the constant of integration, C
7.Find ∫ (15x4 − 1) dx
Answer: 3x5 − x + C
- ∫ 15x4 dx = 3x5
- ∫ −1 dx = −x
- Don't forget the constant of integration, C
8.Find ∫ (−8x3 + 1) dx
Answer: −2x4 + x + C
- ∫ −8x3 dx = −2x4
- ∫ 1 dx = x
- Don't forget the constant of integration, C
9.Find ∫ (8x + 2) dx
Answer: 4x2 + 2x + C
- ∫ 8x dx = 4x2
- ∫ 2 dx = 2x
- Don't forget the constant of integration, C
10.Find ∫ (16x3 + 2x) dx
Answer: 4x4 + x2 + C
- ∫ 16x3 dx = 4x4
- ∫ 2x dx = x2
- Don't forget the constant of integration, C
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