CAIE A-Level Mathematics 1.8.2 Constant of Integration

CAIE A-Level Mathematics 1.8.2 Constant of Integration
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise recovering a curve from its derivative, retaining + c and using a given point or stationary-point condition to determine the constant before finding further coordinates.

How this is tested

  • integrate every derivative term and include + c before using any coordinate information
  • substitute the given point into the antiderivative and solve the resulting equation for c
  • use the completed curve equation to calculate another coordinate or verify a stated point

Question 4(b)

[Maximum number: 5]

The equation of a curve is such that dy dx=kx3+2x2\frac{\mathrm{d} y}{\mathrm{~d} x}=k x^{3}+\frac{2}{x^{2}}, where k is a constant. The curve passes through the point S(2,20) and the gradient of the curve at S is 652\frac{65}{2}.

The coordinates of a point T on the curve are (1, t).

Find the value of t.