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Year 11 Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — Answers

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Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Calculus

Year 11 Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — Answers

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

1.Evaluate ∫ from 0 to 2 of (20x4 − 6x − 2) dx

Answer: 112

  1. ∫ 20x4 dx = 4x5
  2. ∫ −6x dx = −3x2
  3. ∫ −2 dx = −2x
  4. F(x) = 4x5 − 3x2 − 2x
  5. F(2) − F(0) = 112 − (0) = 112
2.Find ∫ (4x3 − 3x2 − 2) dx

Answer: x4 − x3 − 2x + C

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

Answer: 2x5 + x4 + 4x + C

  1. ∫ 10x4 dx = 2x5
  2. ∫ 4x3 dx = x4
  3. ∫ 4 dx = 4x
  4. Don't forget the constant of integration, C
4.Evaluate ∫ from 0 to 2 of (−9x2 + 4x − 3) dx

Answer: −22

  1. ∫ −9x2 dx = −3x3
  2. ∫ 4x dx = 2x2
  3. ∫ −3 dx = −3x
  4. F(x) = −3x3 + 2x2 − 3x
  5. F(2) − F(0) = −22 − (0) = −22
5.Evaluate ∫ from 0 to 3 of (−3x2 − 4x + 4) dx

Answer: −33

  1. ∫ −3x2 dx = −x3
  2. ∫ −4x dx = −2x2
  3. ∫ 4 dx = 4x
  4. F(x) = −x3 − 2x2 + 4x
  5. F(3) − F(0) = −33 − (0) = −33
6.Find ∫ (20x4 − 3x2 − 4x) dx

Answer: 4x5 − x3 − 2x2 + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ −3x2 dx = −x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
7.Evaluate ∫ from 0 to 2 of (−15x4 − 12x3 − 4x) dx

Answer: −152

  1. ∫ −15x4 dx = −3x5
  2. ∫ −12x3 dx = −3x4
  3. ∫ −4x dx = −2x2
  4. F(x) = −3x5 − 3x4 − 2x2
  5. F(2) − F(0) = −152 − (0) = −152
8.Evaluate ∫ from 2 to 5 of (12x3 + 12x2 + 4x) dx

Answer: 2337

  1. ∫ 12x3 dx = 3x4
  2. ∫ 12x2 dx = 4x3
  3. ∫ 4x dx = 2x2
  4. F(x) = 3x4 + 4x3 + 2x2
  5. F(5) − F(2) = 2425 − (88) = 2337
9.Evaluate ∫ from 0 to 3 of (−8x3 + 6x2 − 4x) dx

Answer: −126

  1. ∫ −8x3 dx = −2x4
  2. ∫ 6x2 dx = 2x3
  3. ∫ −4x dx = −2x2
  4. F(x) = −2x4 + 2x3 − 2x2
  5. F(3) − F(0) = −126 − (0) = −126
10.Find ∫ (3x2 − 6x + 3) dx

Answer: x3 − 3x2 + 3x + C

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