WMA11/01 Jun 2021, Question 4: Integration: Undoing Differentiation
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks
The question, in short
Integrate the product (3√x + 2)(x − 5) divided by 4√x with respect to x, giving each term in its simplest form.
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Solution · 6 marks
- 1(3√x + 2)(x − 5) = 3x^(3/2) − 15x^(1/2) + 2x − 10
- 2Divide by 4x^(1/2): (3/4)x − 15/4 + (1/2)x^(1/2) − (5/2)x^(−1/2)
- 3Integrate each term: (3/4)(x²/2) − (15/4)x + (1/2)(x^(3/2) ÷ 3/2) − (5/2)(x^(1/2) ÷ 1/2)
- 4= (3/8)x² − (15/4)x + (1/3)x^(3/2) − 5x^(1/2) + C
Answer(3/8)x² − (15/4)x + (1/3)x^(3/2) − 5x^(1/2) + C
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