Success TutoringWorksheets

Year 11 Integration (Polynomials) Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 11 calculus worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Calculus

Year 11 Integration (Polynomials) Worksheet — Level 2 — Practice Set 4 — Answers

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

1.Find ∫ (−15x4 + 12x2 + 2x) dx

Answer: −3x5 + 4x3 + x2 + C

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

Answer: x5 + 4x3 − 2x2 + C

  1. ∫ 5x4 dx = x5
  2. ∫ 12x2 dx = 4x3
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
3.Find ∫ (−10x4 + 8x3 + 12x2) dx

Answer: −2x5 + 2x4 + 4x3 + C

  1. ∫ −10x4 dx = −2x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ 12x2 dx = 4x3
  4. Don't forget the constant of integration, C
4.Find ∫ (−5x4 + 12x3 − 3x2) dx

Answer: −x5 + 3x4 − x3 + C

  1. ∫ −5x4 dx = −x5
  2. ∫ 12x3 dx = 3x4
  3. ∫ −3x2 dx = −x3
  4. Don't forget the constant of integration, C
5.Find ∫ (8x3 − 3x2 + 1) dx

Answer: 2x4 − x3 + x + C

  1. ∫ 8x3 dx = 2x4
  2. ∫ −3x2 dx = −x3
  3. ∫ 1 dx = x
  4. Don't forget the constant of integration, C
6.Find ∫ (15x4 + 8x3 − 3x2) dx

Answer: 3x5 + 2x4 − x3 + C

  1. ∫ 15x4 dx = 3x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ −3x2 dx = −x3
  4. Don't forget the constant of integration, C
7.Find ∫ (−10x4 − 4x + 3) dx

Answer: −2x5 − 2x2 + 3x + C

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

Answer: x3 + x2 − x + C

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

Answer: −2x5 + 3x3 − 2x2 + C

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

Answer: 2x5 + 2x4 − 2x2 + C

  1. ∫ 10x4 dx = 2x5
  2. ∫ 8x3 dx = 2x4
  3. ∫ −4x dx = −2x2
  4. Don't forget the constant of integration, C
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: