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

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

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

1.Find ∫ (5x4 − 9x2 + 2) dx

Answer: x5 − 3x3 + 2x + C

  1. ∫ 5x4 dx = x5
  2. ∫ −9x2 dx = −3x3
  3. ∫ 2 dx = 2x
  4. Don't forget the constant of integration, C
2.Evaluate ∫ from 0 to 2 of (10x4 − 12x3 + 3) dx

Answer: 22

  1. ∫ 10x4 dx = 2x5
  2. ∫ −12x3 dx = −3x4
  3. ∫ 3 dx = 3x
  4. F(x) = 2x5 − 3x4 + 3x
  5. F(2) − F(0) = 22 − (0) = 22
3.Find ∫ (−10x4 + 4x3 − 9x2) dx

Answer: −2x5 + x4 − 3x3 + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 4x3 dx = x4
  3. ∫ −9x2 dx = −3x3
  4. Don't forget the constant of integration, C
4.Evaluate ∫ from 2 to 4 of (15x4 + 12x2 − 4x) dx

Answer: 3176

  1. ∫ 15x4 dx = 3x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ −4x dx = −2x2
  4. F(x) = 3x5 + 4x3 − 2x2
  5. F(4) − F(2) = 3296 − (120) = 3176
5.Find ∫ (−3x2 + 8x − 1) dx

Answer: −x3 + 4x2 − x + C

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

Answer: 958

  1. ∫ 15x4 dx = 3x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ −2x dx = −x2
  4. F(x) = 3x5 + 3x4 − x2
  5. F(3) − F(1) = 963 − (5) = 958
7.Evaluate ∫ from 2 to 5 of (−15x4 + 6x + 4) dx

Answer: −9204

  1. ∫ −15x4 dx = −3x5
  2. ∫ 6x dx = 3x2
  3. ∫ 4 dx = 4x
  4. F(x) = −3x5 + 3x2 + 4x
  5. F(5) − F(2) = −9280 − (−76) = −9204
8.Evaluate ∫ from 2 to 3 of (8x3 − 2x + 1) dx

Answer: 126

  1. ∫ 8x3 dx = 2x4
  2. ∫ −2x dx = −x2
  3. ∫ 1 dx = x
  4. F(x) = 2x4 − x2 + x
  5. F(3) − F(2) = 156 − (30) = 126
9.Find ∫ (10x4 + 3x2 + 8x) dx

Answer: 2x5 + x3 + 4x2 + C

  1. ∫ 10x4 dx = 2x5
  2. ∫ 3x2 dx = x3
  3. ∫ 8x dx = 4x2
  4. Don't forget the constant of integration, C
10.Evaluate ∫ from 0 to 3 of (20x4 + 12x2 + 8x) dx

Answer: 1116

  1. ∫ 20x4 dx = 4x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ 8x dx = 4x2
  4. F(x) = 4x5 + 4x3 + 4x2
  5. F(3) − F(0) = 1116 − (0) = 1116
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