M2_Bk2_Sol_Ch08.1-8.3_E.pdf

M2_Bk2_Sol_Ch08.1-8.3_E.pdf - 8 New Progress in Senior...

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© Hong Kong Educational Publishing Co. 2 New Progress in Senior Mathematics Module 2 Book 2 (Extended Part) Solution Guide 8 8 pp.3 – 21 p.3 1. C x + 3 2. C x + + 4 2 3. C x + 3 sin 4. C e x + 2 p.12 1. Let u = ax + b . Then a dx du = . ) cos( b ax dx d + ) sin( cos ) ( ) cos( ) ( b ax a dx du u du d b ax dx d b ax b ax d d + = = + + + = + + = + C b ax a dx b ax ) cos( 1 ) sin( 2. (a) C x + + 8 ) 3 ( 8 1 (b) C x + 6 ) 3 2 ( 12 1 (c) C x + 3 ) 4 1 ( 12 1 (d) C x + + 2 3 ) 5 2 ( 3 1 p.21 (b) , 2 xdx du u 2 1 (c) , 8 dx du u 2 sec 8 1 (d) , 2 xdx udu sin 2 1 (e) , sin x xdx cos pp.6 – 42 8.1 + dx x x 2 3 3 5 p.6 + = dx x dx dx x 2 3 3 5 + + + + = 3 1 2 1 4 1 3 ) 5 ( 4 C x C x C x C x x x + + + = 3 5 4 4 8.2 du u u 1 2 1 8 3 p.6 du u u u u + + = 1 2 1 ) 1 )( 2 ( ) 2 ( ) 1 2 ( 2 2 + + = du u u ) 1 2 4 ( 2 + + = du udu du u 2 4 2 C u u u + + + = 2 2 3 4 2 3 C u u u + + + = 2 3 3 4 8.3 dx x x 2 2 ) 1 3 ( p.7 + = dx x x x 2 2 1 6 9 + = dx x x ) 6 9 ( 2 1 + = dx x dx x dx 2 1 6 9 C x x x + + = 1 ln 6 9 1 C x x x + = 1 ln 6 9 8.4 + + dx e e x x ) 5 ( 2 p.7 + = dx dx e dx e e x x 5 2 C x e e e x x + + = 5 2 C x e e x x + + = + 5 2 8.5 + θ θ θ d 2 sin cos 1 p.8 + = θ θ θ θ θ d sin 1 sin cos sin 1 2 + = θ θ θ θ d ) csc cot (csc 2 C + = θ θ csc cot Indefinite Integrals
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3 © Hong Kong Educational Publishing Co. Indefinite Integrals 8.6 (a) ) ( ln ) (ln x dx d x x dx d x dx dy + = p.8 x x x x ln 1 ) 1 )( (ln 1 + = + = (b) By (a) , + = + C x x dx x ln ) ln 1 ( + = + C x x xdx dx ln ln + = + + C x x xdx C x ln ln 2 + = C x x x xdx ln ln 8.7 + dx x 9 5 p.13 + = dx x 2 1 ) 9 5 ( C x + + + = + 1 2 1 5 ) 9 5 ( 1 2 1 C x + + = 2 3 ) 9 5 ( 15 2 8.8 + dx x x 1 4 3 4 1 p.13 dx x x x x x x 1 4 3 4 1 4 3 4 1 4 3 4 1 + + + + + = + + + = dx x x x x ) 1 4 ( ) 3 4 ( 1 4 3 4 + + = dx x x ) 1 4 3 4 ( 4 1 C x x + + + + = + + 1 2 1 1 2 1 ) 1 4 ( 1 2 1 4 4 1 ) 3 4 ( 1 2 1 4 4 1 C x x + + + = 2 3 2 3 ) 1 4 ( ) 3 4 ( 24 1 8.9 + dx x x x 14 3 10 5 2 p.14 + + = dx x x x ) 7 3 )( 2 ( ) 2 ( 5 = dx x 7 3 5 C x + = 3 7 3 ln 5 C x + = 7 3 ln 3 5 8.10 + dx e e x x 2 ) ( p.14 + + = dx e e x x ) 2 ( 2 2 + + = dx dx e dx e x x 2 2 2 C x e e x x + + + = 2 2 2 2 2 C x e e x x + + = 2 ) ( 2 1 2 2 8.11 2 π + θ θ θ d 3 2 cos 2 p.15 π + = θ θ θ θ d d 2 3 2 cos 2 C + π + = 2 3 2 sin 2 1 2 2 2 θ θ C + π + = 2 3 2 sin 2 1 2 θ θ 8.12 dx x 3 p.15 = dx e x ) ( 3 ln = dx e x ) 3 (ln C e x + = ) 3 (ln 3 ln 1 C x + = 3 ln 3 8.13 = dx x xdx 2 2 cos 1 sin 2 p.16 C x x C x x dx x + = + = = 4 2 sin 2 2 sin 2 1 2 1 2 1 ) 2 cos 1 ( 2 1 8.14 xdx 4 cos p.16 = dx x 2 2 ) (cos + = dx x 2 2 2 cos 1 + + = dx x x ) 2 cos 2 cos 2 1 ( 4 1 2
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