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Year 12 Integration (Polynomials) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 12 calculus worksheet.

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Calculus

Year 12 Integration (Polynomials) Worksheet — Level 2 — Practice Set 3 — Answers

Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.

1.Find ∫ (16x3 + 4x + 1) dx

Answer: 4x4 + 2x2 + x + C

  1. ∫ 16x3 dx = 4x4
  2. ∫ 4x dx = 2x2
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
2.Find ∫ (16x3 − 9x2 − 1) dx

Answer: 4x4 − 3x3 − x + C

  1. ∫ 16x3 dx = 4x4
  2. ∫ −9x2 dx = −3x3
  3. ∫ −1 dx = −x
  4. Don't forget the constant of integration, C
3.Find ∫ (−15x4 − 6x2 − 2x) dx

Answer: −3x5 − 2x3 − x2 + C

  1. ∫ −15x4 dx = −3x5
  2. ∫ −6x2 dx = −2x3
  3. ∫ −2x dx = −x2
  4. Don't forget the constant of integration, C
4.Find ∫ (9x2 + 4x + 3) dx

Answer: 3x3 + 2x2 + 3x + C

  1. ∫ 9x2 dx = 3x3
  2. ∫ 4x dx = 2x2
  3. ∫ 3 dx = 3x
  4. Don't forget the constant of integration, C
5.Find ∫ (−15x4 − 2x − 3) dx

Answer: −3x5 − x2 − 3x + C

  1. ∫ −15x4 dx = −3x5
  2. ∫ −2x dx = −x2
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
6.Find ∫ (15x4 − 8x3 + 6x) dx

Answer: 3x5 − 2x4 + 3x2 + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ 6x dx = 3x2
  4. Don't forget the constant of integration, C
7.Find ∫ (5x4 + 16x3 − 4x) dx

Answer: x5 + 4x4 − 2x2 + C

  1. ∫ 5x4 dx = x5
  2. ∫ 16x3 dx = 4x4
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
8.Find ∫ (−15x4 − 6x − 3) dx

Answer: −3x5 − 3x2 − 3x + C

  1. ∫ −15x4 dx = −3x5
  2. ∫ −6x dx = −3x2
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
9.Find ∫ (−10x4 + 4x3 + 4x) dx

Answer: −2x5 + x4 + 2x2 + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 4x3 dx = x4
  3. ∫ 4x dx = 2x2
  4. Don't forget the constant of integration, C
10.Find ∫ (−10x4 + 8x + 4) dx

Answer: −2x5 + 4x2 + 4x + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 8x dx = 4x2
  3. ∫ 4 dx = 4x
  4. Don't forget the constant of integration, C
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