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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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Year 12 · Mathematics · Calculus

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

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

1.Find ∫ (−4x3 + 2x − 3) dx

Answer: −x4 + x2 − 3x + C

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

Answer: 3x5 − 2x3 − x + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ −6x2 dx = −2x3
  3. ∫ −1 dx = −x
  4. Don't forget the constant of integration, C
3.Find ∫ (−10x4 + 12x3 − 3) dx

Answer: −2x5 + 3x4 − 3x + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
4.Find ∫ (4x3 + 12x2 + 1) dx

Answer: x4 + 4x3 + x + C

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

Answer: 3x4 − x3 + 4x2 + C

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

Answer: x5 − 2x2 − x + C

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

Answer: −2x4 + 2x2 − x + C

  1. ∫ −8x3 dx = −2x4
  2. ∫ 4x dx = 2x2
  3. ∫ −1 dx = −x
  4. Don't forget the constant of integration, C
8.Find ∫ (10x4 + 9x2 − 1) dx

Answer: 2x5 + 3x3 − x + C

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

Answer: −2x5 + x3 + 2x + C

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

Answer: 2x5 + 2x4 − 2x2 + C

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