O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2013 · Q109 Marks
(a) (i) Find ∫√2x - 5dx.
- (a)(i)Find ∫√2x - 5dx.[2]
- (a)(ii)Hence evaluate ∫_3^15 √2x - 5dx.[2]
- (b)(i)Find d/dx (x³lnx).[2]
- (b)(ii)Hence find ∫x²lnxdx.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [1] B1 for k(2x – 5)^(3/2)
- [1] B1 for 1/3 (2x-5)^(3/2)
- [1] M1 for correct use of limits
- [1] 124/3 A1 Allow awrt 41.3
- [1] B1 for each term, allow unsimplified
- [1] B1 for each term, allow unsimplified
- [1] M1 for a use of answer to (i)
- [1] A1 for intergrating x² or dividing by 3
- [1] ∫x² lnx dx = 1/3 x³ lnx - x³/9 (+c) A1
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