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Year 11 Integration (Polynomials) Worksheet — Level 3 — Practice Set 2 — Answers

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Year 11 Integration (Polynomials) Worksheet — Level 3 — Practice Set 2 — Answers

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

1.Find ∫ (20x4 + 8x − 2) dx

Answer: 4x5 + 4x2 − 2x + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ 8x dx = 4x2
  3. ∫ −2 dx = −2x
  4. Don't forget the constant of integration, C
2.Find ∫ (9x2 − 2x + 2) dx

Answer: 3x3 − x2 + 2x + C

  1. ∫ 9x2 dx = 3x3
  2. ∫ −2x dx = −x2
  3. ∫ 2 dx = 2x
  4. Don't forget the constant of integration, C
3.Evaluate ∫ from 0 to 1 of (−10x4 + 12x3 − 2) dx

Answer: −1

  1. ∫ −10x4 dx = −2x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ −2 dx = −2x
  4. F(x) = −2x5 + 3x4 − 2x
  5. F(1) − F(0) = −1 − (0) = −1
4.Evaluate ∫ from 2 to 5 of (−12x3 + 12x2 − 1) dx

Answer: −1362

  1. ∫ −12x3 dx = −3x4
  2. ∫ 12x2 dx = 4x3
  3. ∫ −1 dx = −x
  4. F(x) = −3x4 + 4x3 − x
  5. F(5) − F(2) = −1380 − (−18) = −1362
5.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
6.Evaluate ∫ from 0 to 1 of (−15x4 + 8x3 + 6x) dx

Answer: 2

  1. ∫ −15x4 dx = −3x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ 6x dx = 3x2
  4. F(x) = −3x5 + 2x4 + 3x2
  5. F(1) − F(0) = 2 − (0) = 2
7.Evaluate ∫ from 1 to 3 of (−5x4 − 9x2 + 8x) dx

Answer: −288

  1. ∫ −5x4 dx = −x5
  2. ∫ −9x2 dx = −3x3
  3. ∫ 8x dx = 4x2
  4. F(x) = −x5 − 3x3 + 4x2
  5. F(3) − F(1) = −288 − (0) = −288
8.Evaluate ∫ from 2 to 5 of (−15x4 + 12x2 − 6x) dx

Answer: −8874

  1. ∫ −15x4 dx = −3x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ −6x dx = −3x2
  4. F(x) = −3x5 + 4x3 − 3x2
  5. F(5) − F(2) = −8950 − (−76) = −8874
9.Find ∫ (−10x4 + 6x2 + 4x) dx

Answer: −2x5 + 2x3 + 2x2 + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 6x2 dx = 2x3
  3. ∫ 4x dx = 2x2
  4. Don't forget the constant of integration, C
10.Find ∫ (20x4 + 16x3 − 6x2) dx

Answer: 4x5 + 4x4 − 2x3 + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ 16x3 dx = 4x4
  3. ∫ −6x2 dx = −2x3
  4. Don't forget the constant of integration, C
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