O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2016 · Q97 Marks
Find ∫(x³ + x² + 1) / x² dx.
- (a)Find ∫(x³ + x² + 1) / x² dx.[3]
- (b)(i)Find ∫sin(5x + π)dx.[2]
- (b)(ii)Hence evaluate ∫(from -π/5 to 0) sin(5x + π)dx.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [B3] x²/2 + x - x⁻¹ (+c) isw B1 for each term allow x²/2 + x + x⁻¹ / -1 (+c) isw for B3
- [M1] kcos(5x + π) where k < 0 or -cos(5x + π)/5 or -cos(5x + π)/5 (+c)
- [A1]
- [M1] -cos(5(0)+ π)/5 - (-cos(5(-π/5)+ π)/5) or -cos(π)/5 - (-cos(0)/5) correct substitution of the given limits into their expression of the form kcos(5x+π), dep on M1 in (b)(i)
- [A1] 0.4 oe answer only does not score
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