ANSWERS 477 



XVII (pages 265, 266, 267) 



(1) When x = 0-9, A - 1-80155 



(2) When x - 0-09, A - 0-10567 

 () Whm x o-S, A - 0-7840 



(4) True area 78-51 sq. in., area by Simpson's Rule 78-177 sq. 



in., error 0-458 per cent. ; area by Trapezoidal Rule 77-614 

 sq. in., error 1-171 per cent. 



(5) Area = 31 sq. in., $ = 5-302*, V OY = 1051 cub. in., I OY = 1099 



inch units 



(6) Area = 31-14 sq. in., y = 1-935*, V ox = 378-7 cub. in., Io X 



= 171-1 inch units 



(7) 1st derived fig. 10-11 sq. in., 2nd derived fig. 4-81 sq. in., 



y = 1-94,7", Io X = 173-2 inch units 



(8) 1st derived fig. 18-67 sq. in., 2nd derived fig. 13-59 sq. in., 



x = 5-419", I OY = 1101 inch units 



(9) Area = 36-19 sq. in., x = 4-127", V OY = 938-5 cub. in., IO Y 



= 764-3 inch units 



(10) Area = 36-36 sq. in., y = 2-827", V ox = 645-9 cub. in., IQX 



= 369-5 inch units 



(11) 1st derived fig. 17-025 sq. in., 2nd derived fig. 10-25 sq. in., 



y = 2-809", IQX = 369 inch units 



(12) 1st derived fig. 18-73 sq. in., 2nd derived fig. 12-06 sq. in., 



x = 4-141", IOY = 771-8 inch units 



(13) 1st derived fig. 14-137 sq. in., 2nd derived fig. 8-836 sq. in., 



y = 3", I = 318-09 inch units 



(14) Area = 21-19 sq. in., 1st derived fig. 9-74 sq. in., 2nd derived 



fig. 5-63 sq. in., y = 2-758", I = 202-7 inch units 

 (16) 1268-3 cub. in. (17) h = 8", volume = 1338-9 cub. in. 



(18) (I/I + 4*/2 + 0s) 



XVIII (pages 284, 285) 



(1) 0-5211 (2) 3-418 (3) 2-295 (4) 15-31 (5) 1-062 

 (6) (7) 5-576 (8) 12 (9) 241-3 3-2 (10) 1-479 



(11) 1-222 



2 f. n o *>A 



(12) r = 2a sin tan 0, r 2 = 4a 2 cot 20 cosec 20, r 2 = ^~ 



cos 6 



(13) 64-42 (14) r 2 = 9 cos 20, 4-5 (15) 2-546, 1-386, 1-215 



