2006 Promo Ans.doc - Page 1 of 14 1 Find the integrals 1 2...

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Page 1 of 14 1 Find the integrals (a) 1 1 2 sin 2 1 d x x e x , [2] (b) 2 5 d 16 x x x . [3] 3
(ii) By using the substitution 3tan x , find the exact value of 3 2 0 9 d x x [3] 3 x
2006 TJC JC1 H2 Promo Exam Solution
Page 2 of 14 2 1 9 ln( 2 1) 2 2 3 (i) Given that 3 1 cos y x , show that 2 2 2 2 d d 9 1 3cos d d 2 y y y y x x x and hence obtain the Maclaurin’s series for y up to and including the term in 2 x [5] (ii) By using the series expansion of 2 4 cos 1 2! 4! x x x L , check the correctness of the first 2 terms in the series for y . [2] , .
2006 TJC JC1 H2 Promo Exam Solution
Page 3 of 14 Using 2 3 1 cos y x , y 2 3 2 1 1 2 x 2 3 2 2 x . (verified) 4 An isosceles triangle ABC is shown in the diagram with AC = BC. = 10 cm AB and 30 CAB

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