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11th Grade Integration (Polynomials) Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers

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

1.Evaluate ∫ from 1 to 3 of (−4x3 − 2x + 4) dx

Answer: −80

  1. ∫ −4x3 dx = −x4
  2. ∫ −2x dx = −x2
  3. ∫ 4 dx = 4x
  4. F(x) = −x4 − x2 + 4x
  5. F(3) − F(1) = −78 − (2) = −80
2.Evaluate ∫ from 0 to 2 of (20x4 + 8x3 + 3x2) dx

Answer: 168

  1. ∫ 20x4 dx = 4x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ 3x2 dx = x3
  4. F(x) = 4x5 + 2x4 + x3
  5. F(2) − F(0) = 168 − (0) = 168
3.Evaluate ∫ from 0 to 3 of (20x4 + 4x3 + 4) dx

Answer: 1065

  1. ∫ 20x4 dx = 4x5
  2. ∫ 4x3 dx = x4
  3. ∫ 4 dx = 4x
  4. F(x) = 4x5 + x4 + 4x
  5. F(3) − F(0) = 1065 − (0) = 1065
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 2 of (10x4 + 12x2 − 2) dx

Answer: 88

  1. ∫ 10x4 dx = 2x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ −2 dx = −2x
  4. F(x) = 2x5 + 4x3 − 2x
  5. F(2) − F(1) = 92 − (4) = 88
6.Find ∫ (12x3 + 3x2 − 2) dx

Answer: 3x4 + x3 − 2x + C

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

Answer: −x5 − x3 + 2x + C

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

Answer: 2x4 − x3 + 2x2 + C

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

Answer: 62

  1. ∫ 3x2 dx = x3
  2. ∫ 8x dx = 4x2
  3. ∫ 2 dx = 2x
  4. F(x) = x3 + 4x2 + 2x
  5. F(3) − F(1) = 69 − (7) = 62
10.Evaluate ∫ from 1 to 2 of (−10x4 − 4x3 + 9x2) dx

Answer: −56

  1. ∫ −10x4 dx = −2x5
  2. ∫ −4x3 dx = −x4
  3. ∫ 9x2 dx = 3x3
  4. F(x) = −2x5 − x4 + 3x3
  5. F(2) − F(1) = −56 − (0) = −56
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