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Year 11 Integration (Polynomials) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 11 calculus worksheet.

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Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Calculus

Year 11 Integration (Polynomials) Worksheet — Level 3 — Answers

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

1.Find ∫ (−10x4 − 6x2 − 2) dx

Answer: −2x5 − 2x3 − 2x + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ −6x2 dx = −2x3
  3. ∫ −2 dx = −2x
  4. Don't forget the constant of integration, C
2.Find ∫ (5x4 + 9x2 − 6x) dx

Answer: x5 + 3x3 − 3x2 + C

  1. ∫ 5x4 dx = x5
  2. ∫ 9x2 dx = 3x3
  3. ∫ −6x dx = −3x2
  4. Don't forget the constant of integration, C
3.Find ∫ (−10x4 − 2x − 1) dx

Answer: −2x5 − x2 − x + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ −2x dx = −x2
  3. ∫ −1 dx = −x
  4. Don't forget the constant of integration, C
4.Evaluate ∫ from 1 to 4 of (−5x4 + 4x + 3) dx

Answer: −984

  1. ∫ −5x4 dx = −x5
  2. ∫ 4x dx = 2x2
  3. ∫ 3 dx = 3x
  4. F(x) = −x5 + 2x2 + 3x
  5. F(4) − F(1) = −980 − (4) = −984
5.Evaluate ∫ from 2 to 5 of (20x4 − 12x3 − 6x2) dx

Answer: 10311

  1. ∫ 20x4 dx = 4x5
  2. ∫ −12x3 dx = −3x4
  3. ∫ −6x2 dx = −2x3
  4. F(x) = 4x5 − 3x4 − 2x3
  5. F(5) − F(2) = 10375 − (64) = 10311
6.Find ∫ (15x4 + 12x2 − 4x) dx

Answer: 3x5 + 4x3 − 2x2 + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
7.Find ∫ (8x3 + 3x2 + 6x) dx

Answer: 2x4 + x3 + 3x2 + C

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

Answer: −1599

  1. ∫ −12x3 dx = −3x4
  2. ∫ 6x2 dx = 2x3
  3. ∫ −2 dx = −2x
  4. F(x) = −3x4 + 2x3 − 2x
  5. F(5) − F(2) = −1635 − (−36) = −1599
9.Evaluate ∫ from 0 to 2 of (5x4 + 4x3 + 8x) dx

Answer: 64

  1. ∫ 5x4 dx = x5
  2. ∫ 4x3 dx = x4
  3. ∫ 8x dx = 4x2
  4. F(x) = x5 + x4 + 4x2
  5. F(2) − F(0) = 64 − (0) = 64
10.Find ∫ (−6x2 + 6x − 3) dx

Answer: −2x3 + 3x2 − 3x + C

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