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

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

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Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Calculus

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

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

1.Find ∫ (−5x4 + 8x − 3) dx

Answer: −x5 + 4x2 − 3x + C

  1. ∫ −5x4 dx = −x5
  2. ∫ 8x dx = 4x2
  3. ∫ −3 dx = −3x
  4. Don't forget the constant of integration, C
2.Find ∫ (10x4 − 9x2 − 2) dx

Answer: 2x5 − 3x3 − 2x + C

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

Answer: 2x5 − 2x4 − x2 + C

  1. ∫ 10x4 dx = 2x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ −2x dx = −x2
  4. Don't forget the constant of integration, C
5.Find ∫ (4x3 + 6x2 + 8x) dx

Answer: x4 + 2x3 + 4x2 + C

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

Answer: 70

  1. ∫ 4x3 dx = x4
  2. ∫ −3x2 dx = −x3
  3. ∫ 4x dx = 2x2
  4. F(x) = x4 − x3 + 2x2
  5. F(3) − F(1) = 72 − (2) = 70
7.Find ∫ (12x2 − 4x + 1) dx

Answer: 4x3 − 2x2 + x + C

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

Answer: −58

  1. ∫ −4x3 dx = −x4
  2. ∫ 4x dx = 2x2
  3. ∫ 3 dx = 3x
  4. F(x) = −x4 + 2x2 + 3x
  5. F(3) − F(1) = −54 − (4) = −58
9.Evaluate ∫ from 0 to 1 of (20x4 − 3x2 − 1) dx

Answer: 2

  1. ∫ 20x4 dx = 4x5
  2. ∫ −3x2 dx = −x3
  3. ∫ −1 dx = −x
  4. F(x) = 4x5 − x3 − x
  5. F(1) − F(0) = 2 − (0) = 2
10.Evaluate ∫ from 1 to 3 of (−5x4 − 8x3 + 9x2) dx

Answer: −324

  1. ∫ −5x4 dx = −x5
  2. ∫ −8x3 dx = −2x4
  3. ∫ 9x2 dx = 3x3
  4. F(x) = −x5 − 2x4 + 3x3
  5. F(3) − F(1) = −324 − (0) = −324
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