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11th Grade Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.Find ∫ (−15x4 − 4x3 − 2) dx

Answer: −3x5 − x4 − 2x + C

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

Answer: 2x5 − 2x3 − x + C

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

Answer: −x4 + 4x3 + x2 + C

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

Answer: 55

  1. ∫ 12x3 dx = 3x4
  2. ∫ 8x dx = 4x2
  3. ∫ −2 dx = −2x
  4. F(x) = 3x4 + 4x2 − 2x
  5. F(2) − F(1) = 60 − (5) = 55
5.Find ∫ (−9x2 + 2x − 1) dx

Answer: −3x3 + x2 − x + C

  1. ∫ −9x2 dx = −3x3
  2. ∫ 2x dx = x2
  3. ∫ −1 dx = −x
  4. Don't forget the constant of integration, C
6.Find ∫ (10x4 − 8x3 + 2) dx

Answer: 2x5 − 2x4 + 2x + C

  1. ∫ 10x4 dx = 2x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ 2 dx = 2x
  4. Don't forget the constant of integration, C
7.Evaluate ∫ from 1 to 2 of (4x3 + 9x2 + 8x) dx

Answer: 48

  1. ∫ 4x3 dx = x4
  2. ∫ 9x2 dx = 3x3
  3. ∫ 8x dx = 4x2
  4. F(x) = x4 + 3x3 + 4x2
  5. F(2) − F(1) = 56 − (8) = 48
8.Evaluate ∫ from 1 to 4 of (−9x2 − 6x − 3) dx

Answer: −243

  1. ∫ −9x2 dx = −3x3
  2. ∫ −6x dx = −3x2
  3. ∫ −3 dx = −3x
  4. F(x) = −3x3 − 3x2 − 3x
  5. F(4) − F(1) = −252 − (−9) = −243
9.Find ∫ (−8x3 − 3x2 − 3) dx

Answer: −2x4 − x3 − 3x + C

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

Answer: x4 + 2x3 + 3x2 + C

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