Year 13 Integration (Polynomials) Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (15x4 − 9x2) dx
Answer: 3x5 − 3x3 + C
- ∫ 15x4 dx = 3x5
- ∫ −9x2 dx = −3x3
- Don't forget the constant of integration, C
2.Find ∫ (20x4 + 3) dx
Answer: 4x5 + 3x + C
- ∫ 20x4 dx = 4x5
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
3.Find ∫ (12x3 + 4) dx
Answer: 3x4 + 4x + C
- ∫ 12x3 dx = 3x4
- ∫ 4 dx = 4x
- 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 ∫ (−10x4 − 4x) dx
Answer: −2x5 − 2x2 + C
- ∫ −10x4 dx = −2x5
- ∫ −4x dx = −2x2
- Don't forget the constant of integration, C
6.Find ∫ (8x − 2) dx
Answer: 4x2 − 2x + C
- ∫ 8x dx = 4x2
- ∫ −2 dx = −2x
- Don't forget the constant of integration, C
7.Find ∫ (20x4 − 4x) dx
Answer: 4x5 − 2x2 + C
- ∫ 20x4 dx = 4x5
- ∫ −4x dx = −2x2
- Don't forget the constant of integration, C
8.Find ∫ (5x4 + 16x3) dx
Answer: x5 + 4x4 + C
- ∫ 5x4 dx = x5
- ∫ 16x3 dx = 4x4
- Don't forget the constant of integration, C
9.Find ∫ (3x2 + 1) dx
Answer: x3 + x + C
- ∫ 3x2 dx = x3
- ∫ 1 dx = x
- Don't forget the constant of integration, C
10.Find ∫ (−12x3 + 4x) dx
Answer: −3x4 + 2x2 + C
- ∫ −12x3 dx = −3x4
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
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