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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 ∫ (−15x4 − 4x + 1) dx

Answer: −3x5 − 2x2 + x + C

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

Answer: 404

  1. ∫ 16x3 dx = 4x4
  2. ∫ 6x2 dx = 2x3
  3. ∫ 8x dx = 4x2
  4. F(x) = 4x4 + 2x3 + 4x2
  5. F(3) − F(1) = 414 − (10) = 404
3.Find ∫ (−5x4 + 4x3 − 3x2) dx

Answer: −x5 + x4 − x3 + C

  1. ∫ −5x4 dx = −x5
  2. ∫ 4x3 dx = x4
  3. ∫ −3x2 dx = −x3
  4. Don't forget the constant of integration, C
4.Evaluate ∫ from 0 to 1 of (12x3 + 9x2 + 2) dx

Answer: 8

  1. ∫ 12x3 dx = 3x4
  2. ∫ 9x2 dx = 3x3
  3. ∫ 2 dx = 2x
  4. F(x) = 3x4 + 3x3 + 2x
  5. F(1) − F(0) = 8 − (0) = 8
5.Find ∫ (5x4 − 6x2 − 4x) dx

Answer: x5 − 2x3 − 2x2 + C

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

Answer: 2222

  1. ∫ 10x4 dx = 2x5
  2. ∫ 4x3 dx = x4
  3. ∫ −1 dx = −x
  4. F(x) = 2x5 + x4 − x
  5. F(4) − F(2) = 2300 − (78) = 2222
7.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
8.Evaluate ∫ from 0 to 2 of (−5x4 + 2x − 2) dx

Answer: −32

  1. ∫ −5x4 dx = −x5
  2. ∫ 2x dx = x2
  3. ∫ −2 dx = −2x
  4. F(x) = −x5 + x2 − 2x
  5. F(2) − F(0) = −32 − (0) = −32
9.Find ∫ (9x2 − 6x − 3) dx

Answer: 3x3 − 3x2 − 3x + C

  1. ∫ 9x2 dx = 3x3
  2. ∫ −6x dx = −3x2
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
10.Find ∫ (−5x4 + 8x3 − 9x2) dx

Answer: −x5 + 2x4 − 3x3 + C

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