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Year 12 Integration (Polynomials) Worksheet — Level 2 — 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 — Answers

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

1.Find ∫ (−4x3 + 12x2 − 4x) dx

Answer: −x4 + 4x3 − 2x2 + C

  1. ∫ −4x3 dx = −x4
  2. ∫ 12x2 dx = 4x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
2.Find ∫ (−5x4 − 4x3 + 12x2) dx

Answer: −x5 − x4 + 4x3 + C

  1. ∫ −5x4 dx = −x5
  2. ∫ −4x3 dx = −x4
  3. ∫ 12x2 dx = 4x3
  4. Don't forget the constant of integration, C
3.Find ∫ (16x3 + 8x − 3) dx

Answer: 4x4 + 4x2 − 3x + C

  1. ∫ 16x3 dx = 4x4
  2. ∫ 8x dx = 4x2
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
4.Find ∫ (5x4 + 12x2 + 2) dx

Answer: x5 + 4x3 + 2x + C

  1. ∫ 5x4 dx = x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ 2 dx = 2x
  4. Don't forget the constant of integration, C
5.Find ∫ (4x3 + 2x + 4) dx

Answer: x4 + x2 + 4x + C

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

Answer: x5 + 2x4 + 2x2 + C

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

Answer: x4 − 2x3 + x + C

  1. ∫ 4x3 dx = x4
  2. ∫ −6x2 dx = −2x3
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
8.Find ∫ (20x4 + 12x2 + 8x) dx

Answer: 4x5 + 4x3 + 4x2 + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ 8x dx = 4x2
  4. Don't forget the constant of integration, C
9.Find ∫ (−5x4 − 8x3 − 1) dx

Answer: −x5 − 2x4 − x + C

  1. ∫ −5x4 dx = −x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ −1 dx = −x
  4. Don't forget the constant of integration, C
10.Find ∫ (20x4 + 8x3 + 1) dx

Answer: 4x5 + 2x4 + x + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
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