2026 IGCSE Additional Mathematics February/March 0606/12 Q8

2026 IGCSE Additional Mathematics February/March 0606/12 Q8

12 marks

A curve has equation \(y=xe^{2x+1}\).

  1. Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).[3]
  2. The line \(L\) is the tangent to the curve at the point where \(x=\dfrac12\).
    Find the exact coordinates of the two points where \(L\) meets the axes.[5]
  3. Use your answer to 8(a) to find \(\int xe^{2x+1}\,\mathrm{d}x\).[4]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \((1+2x)e^{2x+1}\) (b) \(\left(\dfrac14,0\right)\), \(\left(0,-\dfrac{e^2}{2}\right)\) (c) \(\dfrac{2x-1}{4}e^{2x+1}+C\)

Need help? Join our JC Math tuition classes.

Learn more