Year 12 Integration (Polynomials) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Year 12 · Mathematics · Calculus
Year 12 Integration (Polynomials) Worksheet — Level 1 — Answers
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Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (−4x3 + 4x) dx
Answer: −x4 + 2x2 + C
- ∫ −4x3 dx = −x4
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
2.Find ∫ (−5x4 + 6x2) dx
Answer: −x5 + 2x3 + C
- ∫ −5x4 dx = −x5
- ∫ 6x2 dx = 2x3
- Don't forget the constant of integration, C
3.Find ∫ (−9x2 + 3) dx
Answer: −3x3 + 3x + C
- ∫ −9x2 dx = −3x3
- ∫ 3 dx = 3x
- Don't forget the constant of integration, C
4.Find ∫ (−10x4 − 8x3) dx
Answer: −2x5 − 2x4 + C
- ∫ −10x4 dx = −2x5
- ∫ −8x3 dx = −2x4
- Don't forget the constant of integration, C
5.Find ∫ (16x3 − 1) dx
Answer: 4x4 − x + C
- ∫ 16x3 dx = 4x4
- ∫ −1 dx = −x
- Don't forget the constant of integration, C
6.Find ∫ (−2x − 3) dx
Answer: −x2 − 3x + C
- ∫ −2x dx = −x2
- ∫ −3 dx = −3x
- Don't forget the constant of integration, C
7.Find ∫ (15x4 + 4x3) dx
Answer: 3x5 + x4 + C
- ∫ 15x4 dx = 3x5
- ∫ 4x3 dx = x4
- Don't forget the constant of integration, C
8.Find ∫ (−6x2 − 4x) dx
Answer: −2x3 − 2x2 + C
- ∫ −6x2 dx = −2x3
- ∫ −4x dx = −2x2
- Don't forget the constant of integration, C
9.Find ∫ (−3x2 − 1) dx
Answer: −x3 − x + C
- ∫ −3x2 dx = −x3
- ∫ −1 dx = −x
- Don't forget the constant of integration, C
10.Find ∫ (−12x3 + 4x) dx
Answer: −3x4 + 2x2 + C
- ∫ −12x3 dx = −3x4
- ∫ 4x dx = 2x2
- Don't forget the constant of integration, C
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