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Year 13 Integration (Polynomials) Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 13 calculus worksheet.

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Year 13 · Mathematics · Calculus

Year 13 Integration (Polynomials) Worksheet — Level 2 — Answers

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

1.Find ∫ (12x3 − 2x + 3) dx

Answer: 3x4 − x2 + 3x + C

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

Answer: 4x3 − x2 + 4x + C

  1. ∫ 12x2 dx = 4x3
  2. ∫ −2x dx = −x2
  3. ∫ 4 dx = 4x
  4. Don't forget the constant of integration, C
3.Find ∫ (15x4 + 8x3 + 4) dx

Answer: 3x5 + 2x4 + 4x + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ 4 dx = 4x
  4. Don't forget the constant of integration, C
4.Find ∫ (20x4 − 4x + 2) dx

Answer: 4x5 − 2x2 + 2x + C

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

Answer: 2x4 + 4x3 + x2 + C

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

Answer: x4 + 3x3 − 2x2 + C

  1. ∫ 4x3 dx = x4
  2. ∫ 9x2 dx = 3x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
7.Find ∫ (15x4 + 12x3 + 4) dx

Answer: 3x5 + 3x4 + 4x + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ 4 dx = 4x
  4. Don't forget the constant of integration, C
8.Find ∫ (5x4 − 12x3 + 3) dx

Answer: x5 − 3x4 + 3x + C

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

Answer: 4x3 − x2 + x + C

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

Answer: x4 − 2x3 + 4x + C

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