O-LevelAdditional MathematicsDifferentiation and integration4037/21 · Oct/Nov 2011 · Q45 Marks
Given that y = 1/(x² + 3), show that dy/dx = -kx / (x² + 3)², where k is a constant to be found.
- (i)Given that y = 1/(x² + 3), show that dy/dx = -kx / (x² + 3)², where k is a constant to be found.[2]
- (ii)Hence find ∫ 6x/(x² + 3)² dx and evaluate ∫₁³ 6x/(x² + 3)² dx.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [1] kx / (x²+3)²
- [1] k = -2
- [1] 6/(-2) × 1/(x²+3)
- [1] Correct use of limits in C/(x²+3)
- [1] 0.5
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