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

Answer sheet with worked solutions for the 11th Grade calculus worksheet.

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

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

1.Find ∫ (15x4 + 12x2 + 2) dx

Answer: 3x5 + 4x3 + 2x + C

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

Answer: 2x5 − 3x4 + x + C

  1. ∫ 10x4 dx = 2x5
  2. ∫ −12x3 dx = −3x4
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
3.Evaluate ∫ from 0 to 1 of (4x3 + 9x2 + 6x) dx

Answer: 7

  1. ∫ 4x3 dx = x4
  2. ∫ 9x2 dx = 3x3
  3. ∫ 6x dx = 3x2
  4. F(x) = x4 + 3x3 + 3x2
  5. F(1) − F(0) = 7 − (0) = 7
4.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
5.Find ∫ (5x4 + 12x3 − 3) dx

Answer: x5 + 3x4 − 3x + C

  1. ∫ 5x4 dx = x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
6.Find ∫ (−12x3 + 6x2 − 6x) dx

Answer: −3x4 + 2x3 − 3x2 + C

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

Answer: 3x4 − x2 + x + C

  1. ∫ 12x3 dx = 3x4
  2. ∫ −2x dx = −x2
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
8.Evaluate ∫ from 2 to 4 of (20x4 + 2x + 1) dx

Answer: 3982

  1. ∫ 20x4 dx = 4x5
  2. ∫ 2x dx = x2
  3. ∫ 1 dx = x
  4. F(x) = 4x5 + x2 + x
  5. F(4) − F(2) = 4116 − (134) = 3982
9.Find ∫ (−4x3 + 4x + 1) dx

Answer: −x4 + 2x2 + x + C

  1. ∫ −4x3 dx = −x4
  2. ∫ 4x dx = 2x2
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
10.Evaluate ∫ from 0 to 1 of (−12x3 − 6x2 − 2) dx

Answer: −7

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