Quelpr
7 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 6(b)

The gradient function for a curve y = f(x) is given as dy/dx = -y/x. Given that the curve passes through the point (1,1), determine an expression for f(x).

Given that the curve passes through the point (1,1), determine an expression for f(x).

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 6(a)(i)Determine the area of the region, A.[3 marks]
  2. 6(a)(ii)Calculate the volume of the solid that results from revolving the region, A, about the x-axis.[5 marks]
  3. 6(c)By using the substitution, y = x², show that ∫ 1/(√y + √y³) dy = ∫ 2/(1 + x²) dx.[5 marks]
  4. 6(d)find ∫sin²x cos²x dx.[5 marks]

More practice: the rest of this paper · more Integration I questions · all CAPE Pure Mathematics Unit 1 past papers