Year 11 Integration (Polynomials) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Year 11 · Mathematics · Calculus
Year 11 Integration (Polynomials) Worksheet — Level 1 — Answers
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Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (−10x4 + 6x2) dx
Answer: −2x5 + 2x3 + C
- ∫ −10x4 dx = −2x5
- ∫ 6x2 dx = 2x3
- Don't forget the constant of integration, C
2.Find ∫ (16x3 − 6x) dx
Answer: 4x4 − 3x2 + C
- ∫ 16x3 dx = 4x4
- ∫ −6x dx = −3x2
- Don't forget the constant of integration, C
3.Find ∫ (4x − 3) dx
Answer: 2x2 − 3x + C
- ∫ 4x dx = 2x2
- ∫ −3 dx = −3x
- Don't forget the constant of integration, C
4.Find ∫ (20x4 − 3x2) dx
Answer: 4x5 − x3 + C
- ∫ 20x4 dx = 4x5
- ∫ −3x2 dx = −x3
- Don't forget the constant of integration, C
5.Find ∫ (−5x4 − 12x3) dx
Answer: −x5 − 3x4 + C
- ∫ −5x4 dx = −x5
- ∫ −12x3 dx = −3x4
- Don't forget the constant of integration, C
6.Find ∫ (5x4 − 12x3) dx
Answer: x5 − 3x4 + C
- ∫ 5x4 dx = x5
- ∫ −12x3 dx = −3x4
- Don't forget the constant of integration, C
7.Find ∫ (4x3 − 2x) dx
Answer: x4 − x2 + C
- ∫ 4x3 dx = x4
- ∫ −2x dx = −x2
- Don't forget the constant of integration, C
8.Find ∫ (8x + 3) dx
Answer: 4x2 + 3x + C
- ∫ 8x dx = 4x2
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
9.Find ∫ (−12x3 − 2) dx
Answer: −3x4 − 2x + C
- ∫ −12x3 dx = −3x4
- ∫ −2 dx = −2x
- Don't forget the constant of integration, C
10.Find ∫ (−10x4 + 2x) dx
Answer: −2x5 + x2 + C
- ∫ −10x4 dx = −2x5
- ∫ 2x dx = x2
- Don't forget the constant of integration, C
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