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12th Grade Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — Answers

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

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12th Grade Integration (Polynomials) Worksheet — Level 3 — Practice Set 4 — Answers

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

1.Evaluate ∫ from 1 to 2 of (15x4 + 3x2 − 6x) dx

Answer: 91

  1. ∫ 15x4 dx = 3x5
  2. ∫ 3x2 dx = x3
  3. ∫ −6x dx = −3x2
  4. F(x) = 3x5 + x3 − 3x2
  5. F(2) − F(1) = 92 − (1) = 91
2.Evaluate ∫ from 0 to 3 of (15x4 − 3x2 − 1) dx

Answer: 699

  1. ∫ 15x4 dx = 3x5
  2. ∫ −3x2 dx = −x3
  3. ∫ −1 dx = −x
  4. F(x) = 3x5 − x3 − x
  5. F(3) − F(0) = 699 − (0) = 699
3.Evaluate ∫ from 2 to 5 of (20x4 + 4x3 + 8x) dx

Answer: 13065

  1. ∫ 20x4 dx = 4x5
  2. ∫ 4x3 dx = x4
  3. ∫ 8x dx = 4x2
  4. F(x) = 4x5 + x4 + 4x2
  5. F(5) − F(2) = 13225 − (160) = 13065
4.Evaluate ∫ from 2 to 3 of (10x4 − 12x3 − 6x2) dx

Answer: 189

  1. ∫ 10x4 dx = 2x5
  2. ∫ −12x3 dx = −3x4
  3. ∫ −6x2 dx = −2x3
  4. F(x) = 2x5 − 3x4 − 2x3
  5. F(3) − F(2) = 189 − (0) = 189
5.Find ∫ (−10x4 − 3x2 − 4x) dx

Answer: −2x5 − x3 − 2x2 + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ −3x2 dx = −x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
6.Find ∫ (−5x4 + 4x3 − 9x2) dx

Answer: −x5 + x4 − 3x3 + C

  1. ∫ −5x4 dx = −x5
  2. ∫ 4x3 dx = x4
  3. ∫ −9x2 dx = −3x3
  4. Don't forget the constant of integration, C
7.Find ∫ (−15x4 + 12x3 + 1) dx

Answer: −3x5 + 3x4 + x + C

  1. ∫ −15x4 dx = −3x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
8.Evaluate ∫ from 0 to 1 of (−15x4 − 4x3 − 6x2) dx

Answer: −6

  1. ∫ −15x4 dx = −3x5
  2. ∫ −4x3 dx = −x4
  3. ∫ −6x2 dx = −2x3
  4. F(x) = −3x5 − x4 − 2x3
  5. F(1) − F(0) = −6 − (0) = −6
9.Evaluate ∫ from 1 to 3 of (−5x4 − 4x3 + 9x2) dx

Answer: −244

  1. ∫ −5x4 dx = −x5
  2. ∫ −4x3 dx = −x4
  3. ∫ 9x2 dx = 3x3
  4. F(x) = −x5 − x4 + 3x3
  5. F(3) − F(1) = −243 − (1) = −244
10.Find ∫ (−5x4 − 12x3 − 4x) dx

Answer: −x5 − 3x4 − 2x2 + C

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