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Year 12 Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — Answers

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Calculus

Year 12 Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — Answers

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

1.Find ∫ (−10x4 + 6x2 + 4) dx

Answer: −2x5 + 2x3 + 4x + C

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

Answer: 3x5 + x4 + x3 + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ 4x3 dx = x4
  3. ∫ 3x2 dx = x3
  4. Don't forget the constant of integration, C
3.Evaluate ∫ from 0 to 2 of (−8x3 + 9x2 + 8x) dx

Answer: 8

  1. ∫ −8x3 dx = −2x4
  2. ∫ 9x2 dx = 3x3
  3. ∫ 8x dx = 4x2
  4. F(x) = −2x4 + 3x3 + 4x2
  5. F(2) − F(0) = 8 − (0) = 8
4.Evaluate ∫ from 0 to 3 of (10x4 − 3x2 − 1) dx

Answer: 456

  1. ∫ 10x4 dx = 2x5
  2. ∫ −3x2 dx = −x3
  3. ∫ −1 dx = −x
  4. F(x) = 2x5 − x3 − x
  5. F(3) − F(0) = 456 − (0) = 456
5.Evaluate ∫ from 0 to 2 of (20x4 + 8x3 − 6x) dx

Answer: 148

  1. ∫ 20x4 dx = 4x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ −6x dx = −3x2
  4. F(x) = 4x5 + 2x4 − 3x2
  5. F(2) − F(0) = 148 − (0) = 148
6.Evaluate ∫ from 2 to 5 of (20x4 − 2x + 3) dx

Answer: 12360

  1. ∫ 20x4 dx = 4x5
  2. ∫ −2x dx = −x2
  3. ∫ 3 dx = 3x
  4. F(x) = 4x5 − x2 + 3x
  5. F(5) − F(2) = 12490 − (130) = 12360
7.Find ∫ (10x4 − 3x2 − 2) dx

Answer: 2x5 − x3 − 2x + C

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

Answer: 0

  1. ∫ −3x2 dx = −x3
  2. ∫ 8x dx = 4x2
  3. ∫ 4 dx = 4x
  4. F(x) = −x3 + 4x2 + 4x
  5. F(4) − F(2) = 16 − (16) = 0
9.Find ∫ (20x4 − 3x2 + 2x) dx

Answer: 4x5 − x3 + x2 + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ −3x2 dx = −x3
  3. ∫ 2x dx = x2
  4. Don't forget the constant of integration, C
10.Find ∫ (−12x3 + 6x2 + 2x) dx

Answer: −3x4 + 2x3 + x2 + C

  1. ∫ −12x3 dx = −3x4
  2. ∫ 6x2 dx = 2x3
  3. ∫ 2x dx = x2
  4. Don't forget the constant of integration, C
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