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

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Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Calculus

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

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

1.Find ∫ (−5x4 + 4x3 + 3x2) dx

Answer: −x5 + x4 + x3 + C

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

Answer: 86

  1. ∫ 10x4 dx = 2x5
  2. ∫ 9x2 dx = 3x3
  3. ∫ 2x dx = x2
  4. F(x) = 2x5 + 3x3 + x2
  5. F(2) − F(1) = 92 − (6) = 86
3.Find ∫ (5x4 − 6x2 + 4x) dx

Answer: x5 − 2x3 + 2x2 + C

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

Answer: −2x3 + x2 + 2x + C

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

Answer: −1989

  1. ∫ −10x4 dx = −2x5
  2. ∫ 8x dx = 4x2
  3. ∫ −1 dx = −x
  4. F(x) = −2x5 + 4x2 − x
  5. F(4) − F(1) = −1988 − (1) = −1989
6.Find ∫ (4x3 + 6x + 1) dx

Answer: x4 + 3x2 + x + C

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

Answer: −2x5 + 4x4 + 3x + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 16x3 dx = 4x4
  3. ∫ 3 dx = 3x
  4. Don't forget the constant of integration, C
8.Evaluate ∫ from 2 to 3 of (−5x4 − 2x − 2) dx

Answer: −218

  1. ∫ −5x4 dx = −x5
  2. ∫ −2x dx = −x2
  3. ∫ −2 dx = −2x
  4. F(x) = −x5 − x2 − 2x
  5. F(3) − F(2) = −258 − (−40) = −218
9.Evaluate ∫ from 1 to 4 of (−15x4 + 12x3 − 1) dx

Answer: −2307

  1. ∫ −15x4 dx = −3x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ −1 dx = −x
  4. F(x) = −3x5 + 3x4 − x
  5. F(4) − F(1) = −2308 − (−1) = −2307
10.Find ∫ (20x4 − 6x2 − 2x) dx

Answer: 4x5 − 2x3 − x2 + C

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