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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 + 3x2 + 6x) dx

Answer: −x5 + x3 + 3x2 + C

  1. ∫ −5x4 dx = −x5
  2. ∫ 3x2 dx = x3
  3. ∫ 6x dx = 3x2
  4. Don't forget the constant of integration, C
2.Evaluate ∫ from 2 to 4 of (−15x4 + 2x + 2) dx

Answer: −2960

  1. ∫ −15x4 dx = −3x5
  2. ∫ 2x dx = x2
  3. ∫ 2 dx = 2x
  4. F(x) = −3x5 + x2 + 2x
  5. F(4) − F(2) = −3048 − (−88) = −2960
3.Find ∫ (16x3 − 6x + 3) dx

Answer: 4x4 − 3x2 + 3x + C

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

Answer: −x4 − 2x3 + x + C

  1. ∫ −4x3 dx = −x4
  2. ∫ −6x2 dx = −2x3
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
5.Evaluate ∫ from 0 to 2 of (15x4 + 4x − 2) dx

Answer: 100

  1. ∫ 15x4 dx = 3x5
  2. ∫ 4x dx = 2x2
  3. ∫ −2 dx = −2x
  4. F(x) = 3x5 + 2x2 − 2x
  5. F(2) − F(0) = 100 − (0) = 100
6.Evaluate ∫ from 0 to 2 of (−5x4 + 4x + 3) dx

Answer: −18

  1. ∫ −5x4 dx = −x5
  2. ∫ 4x dx = 2x2
  3. ∫ 3 dx = 3x
  4. F(x) = −x5 + 2x2 + 3x
  5. F(2) − F(0) = −18 − (0) = −18
7.Find ∫ (−12x3 − 6x2 − 3) dx

Answer: −3x4 − 2x3 − 3x + C

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

Answer: −4

  1. ∫ −4x3 dx = −x4
  2. ∫ 6x2 dx = 2x3
  3. ∫ −3 dx = −3x
  4. F(x) = −x4 + 2x3 − 3x
  5. F(2) − F(1) = −6 − (−2) = −4
9.Evaluate ∫ from 1 to 2 of (16x3 − 9x2 − 3) dx

Answer: 36

  1. ∫ 16x3 dx = 4x4
  2. ∫ −9x2 dx = −3x3
  3. ∫ −3 dx = −3x
  4. F(x) = 4x4 − 3x3 − 3x
  5. F(2) − F(1) = 34 − (−2) = 36
10.Find ∫ (16x3 − 6x2 − 4x) dx

Answer: 4x4 − 2x3 − 2x2 + C

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