WMA11/01 Oct 2021, Question 1: Integration: Undoing Differentiation
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks
The question, in short
Integrate 12x³ + 1/(6√x) − 3/(2x⁴) with respect to x, giving each term in its simplest form.
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Solution · 5 marks
- 1Write as powers: 12x³ + ⅙x^(−1/2) − (3/2)x⁻⁴
- 2∫12x³ dx = 12 × x⁴/4 = 3x⁴
- 3∫⅙x^(−1/2) dx = ⅙ × 2x^(1/2) = ⅓x^(1/2)
- 4∫−(3/2)x⁻⁴ dx = −(3/2) × x⁻³/(−3) = ½x⁻³
- 5Answer: 3x⁴ + ⅓x^(1/2) + ½x⁻³ + c
Answer3x⁴ + ⅓x^(1/2) + ½x⁻³ + c (i.e. 3x⁴ + √x/3 + 1/(2x³) + c)
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