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Year 12 Integration (Polynomials) Worksheet — Level 3 — Practice Set 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Calculus

Year 12 Integration (Polynomials) Worksheet — Level 3 — Practice Set 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.Find ∫ (−10x4 − 3x2 + 4x) dx

Answer: −2x5 − x3 + 2x2 + C

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

Answer: 914

  1. ∫ 20x4 dx = 4x5
  2. ∫ −4x3 dx = −x4
  3. ∫ 3x2 dx = x3
  4. F(x) = 4x5 − x4 + x3
  5. F(3) − F(1) = 918 − (4) = 914
4.Evaluate ∫ from 1 to 3 of (4x3 + 12x2 − 2x) dx

Answer: 176

  1. ∫ 4x3 dx = x4
  2. ∫ 12x2 dx = 4x3
  3. ∫ −2x dx = −x2
  4. F(x) = x4 + 4x3 − x2
  5. F(3) − F(1) = 180 − (4) = 176
5.Find ∫ (−8x3 − 6x2 − 3) dx

Answer: −2x4 − 2x3 − 3x + C

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

Answer: −2x5 + x2 + 3x + C

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

Answer: −x5 + x2 + 3x + C

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

Answer: x5 − 2x4 − x3 + C

  1. ∫ 5x4 dx = x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ −3x2 dx = −x3
  4. Don't forget the constant of integration, C
9.Evaluate ∫ from 0 to 3 of (5x4 − 2x − 2) dx

Answer: 228

  1. ∫ 5x4 dx = x5
  2. ∫ −2x dx = −x2
  3. ∫ −2 dx = −2x
  4. F(x) = x5 − x2 − 2x
  5. F(3) − F(0) = 228 − (0) = 228
10.Evaluate ∫ from 2 to 5 of (−4x3 + 2x + 4) dx

Answer: −576

  1. ∫ −4x3 dx = −x4
  2. ∫ 2x dx = x2
  3. ∫ 4 dx = 4x
  4. F(x) = −x4 + x2 + 4x
  5. F(5) − F(2) = −580 − (−4) = −576
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