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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.Evaluate ∫ from 0 to 3 of (−10x4 + 12x2 + 3) dx

Answer: −369

  1. ∫ −10x4 dx = −2x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ 3 dx = 3x
  4. F(x) = −2x5 + 4x3 + 3x
  5. F(3) − F(0) = −369 − (0) = −369
2.Find ∫ (−4x3 − 3x2 + 4x) dx

Answer: −x4 − x3 + 2x2 + C

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

Answer: −3x5 + 3x4 − x3 + C

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

Answer: 218

  1. ∫ 10x4 dx = 2x5
  2. ∫ −12x3 dx = −3x4
  3. ∫ −3x2 dx = −x3
  4. F(x) = 2x5 − 3x4 − x3
  5. F(3) − F(1) = 216 − (−2) = 218
5.Evaluate ∫ from 2 to 3 of (−5x4 + 4x3 + 2x) dx

Answer: −141

  1. ∫ −5x4 dx = −x5
  2. ∫ 4x3 dx = x4
  3. ∫ 2x dx = x2
  4. F(x) = −x5 + x4 + x2
  5. F(3) − F(2) = −153 − (−12) = −141
6.Find ∫ (−5x4 − 2x + 1) dx

Answer: −x5 − x2 + x + C

  1. ∫ −5x4 dx = −x5
  2. ∫ −2x dx = −x2
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
7.Find ∫ (−5x4 + 9x2 − 2x) dx

Answer: −x5 + 3x3 − x2 + C

  1. ∫ −5x4 dx = −x5
  2. ∫ 9x2 dx = 3x3
  3. ∫ −2x dx = −x2
  4. Don't forget the constant of integration, C
8.Find ∫ (−10x4 + 6x + 3) dx

Answer: −2x5 + 3x2 + 3x + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 6x dx = 3x2
  3. ∫ 3 dx = 3x
  4. Don't forget the constant of integration, C
9.Find ∫ (−15x4 − 6x − 2) dx

Answer: −3x5 − 3x2 − 2x + C

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

Answer: 3x5 + 4x4 + 4x2 + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ 16x3 dx = 4x4
  3. ∫ 8x dx = 4x2
  4. Don't forget the constant of integration, C
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