F.5 DEFINITE INTEGRATION 2條

圖片參考：http://imgcld.yimg.com/8/n/HA00482599/o/701201300040113873432921.jpg


---------------------------------------------------------------------------------------------------

2012-01-30 15:19:21 補充：
當個 integrand 包含 square root , 而入面又係 quadratic polynomial 既時候
可利用 trigonometry 既 substitution 黎消去個 square root
(sinx)^2 + (cosx)^2 = 1
1 + (tanx)^2 = (secx)^2
1 + (cotx)^2 = (cscx)^2

2012-01-31 12:44:37 補充：
sec( sec^-1(5/3) ) = 5 / 3
所以
sec^2 ( sec^-1(5/3) ) = 25/9

2012-01-31 17:01:58 補充：
SEC^-1 即係 SEC 既 INVERSE

就好像 sin30度 = 0.5
咁 sin^-1 (0.5) 就 = 30度
所以 sin^-1 ( sin30度 ) = sin^-1 ( 0.5 ) = 30度

同樣道理 , 若設 x = sec^-1 (5/3) . 咁即係 sec x = 5/3

2012-01-31 17:04:26 補充：
這裡可加深你對INVERSE OF TRIGONOMETRY 的理解

http://en.wikipedia.org/wiki/Inverse_trigonometric_functions

sec^-1 即是 arcsec

hung's answers are correct.
Simon YAU, MSc in Math