Edexcel_WS_C4_PaperL

Edexcel_WS_C4_PaperL - Worked Solutions Edexcel C4 Paper L...

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Worked Solutions Edexcel C4 Paper L 1. # 1 y d y = # 2 x d x ln y = x 2 + c y = e ,x = 1 : ln e = 1 + c c = 0 ln y = x 2 y = e x 2 (4) y x 1 (2) 2. ( a ) V = π # y 2 d x = π # 0 2 (t 2 + 1 ) 2 d x d t d t d x d t = 1 (5) ( b ) π # 0 2 t 2 + 1 2 d t = π # 0 2 t 4 + 2 t 2 + 1 d t = π " t 5 5 + 2 3 t 3 + t # 0 2 = π ± 0 ² 1 5 ( 32 ) + 2 3 ( 8 ) + ( 2 ) ³´ = 206 15 π (2) 3. ( a ) (π, 0 ) (1) ( b ) d y d x = x cos x + sin x when x = 2 . 02 , d y d x 0 . 02 when x = 2 . 04 , d y d x ≈− 0 . 03 (4) ( c ) Area = # π 0 x sin x d x = # π 0 x d d x ( cos x) d x = h x cos x µ π 0 # π 0 ( cos d x = h x cos x + sin x µ π 0 = π (4) 4. ( a )1 7 17 2 1 17 2 ! 1 2 = 17 17 h ( 17 1 )( 17 + 1 ) µ 1 2 = 16 18 = 4 18 = 4 9 × 2 = 12 2 (3) ( b ) ( 1 1 2 = 1 + 1 2 ( + 1 2 ² 1 2 ³ 2 ( 2 = 1 1 2 x 1 8 x 2 ... (2) ( c ) put x = 1 17 2 , ² 1 1 17 2 ³ 1 2 1 1 2 · 1 17 2 577 578 17 ² 577 578 ³ 12 2 2 17 12 × 577 578 34 2 577 408 (5)

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5. ( a ) # x d d x ± 1 k sin kx ² d x = x k sin 1 k # sin d x = x k sin + 1 k 2 cos + c (4) ( b ) ³ x 2 sin 2 x + 1 4 cos 2 x ´ π 4 0 = π 8 sin π 2 + 0 ± 0 + 1 4 ² = 1 8 2 ) (4) ( c ) cos 2 x =
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Edexcel_WS_C4_PaperL - Worked Solutions Edexcel C4 Paper L...

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