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12th Grade Integration (Polynomials) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 12th Grade calculus worksheet.

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Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Calculus

12th Grade Integration (Polynomials) Worksheet — Level 3 — Answers

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

1.Find ∫ (−12x3 + 6x2 − 2) dx

Answer: −3x4 + 2x3 − 2x + C

  1. ∫ −12x3 dx = −3x4
  2. ∫ 6x2 dx = 2x3
  3. ∫ −2 dx = −2x
  4. Don't forget the constant of integration, C
2.Evaluate ∫ from 2 to 4 of (−5x4 − 8x3 − 3x2) dx

Answer: −1528

  1. ∫ −5x4 dx = −x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ −3x2 dx = −x3
  4. F(x) = −x5 − 2x4 − x3
  5. F(4) − F(2) = −1600 − (−72) = −1528
3.Evaluate ∫ from 1 to 4 of (−15x4 + 12x3 + 2x) dx

Answer: −2289

  1. ∫ −15x4 dx = −3x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ 2x dx = x2
  4. F(x) = −3x5 + 3x4 + x2
  5. F(4) − F(1) = −2288 − (1) = −2289
4.Find ∫ (−15x4 − 6x − 3) dx

Answer: −3x5 − 3x2 − 3x + C

  1. ∫ −15x4 dx = −3x5
  2. ∫ −6x dx = −3x2
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
5.Find ∫ (20x4 − 6x + 3) dx

Answer: 4x5 − 3x2 + 3x + C

  1. ∫ 20x4 dx = 4x5
  2. ∫ −6x dx = −3x2
  3. ∫ 3 dx = 3x
  4. Don't forget the constant of integration, C
6.Find ∫ (−12x3 + 4x − 3) dx

Answer: −3x4 + 2x2 − 3x + C

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

Answer: 87

  1. ∫ 4x3 dx = x4
  2. ∫ 8x dx = 4x2
  3. ∫ 2 dx = 2x
  4. F(x) = x4 + 4x2 + 2x
  5. F(3) − F(2) = 123 − (36) = 87
8.Find ∫ (20x4 + 2x − 2) dx

Answer: 4x5 + x2 − 2x + C

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

Answer: −x4 + x3 − 2x2 + C

  1. ∫ −4x3 dx = −x4
  2. ∫ 3x2 dx = x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
10.Evaluate ∫ from 0 to 3 of (10x4 + 16x3 − 3) dx

Answer: 801

  1. ∫ 10x4 dx = 2x5
  2. ∫ 16x3 dx = 4x4
  3. ∫ −3 dx = −3x
  4. F(x) = 2x5 + 4x4 − 3x
  5. F(3) − F(0) = 801 − (0) = 801
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