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T sin x, = Jo 1+sin x, T sin x, 21 = J. 1+sin x, sin x, dx, Jo 1+sin x, 21 = T, 1, dx, 1+sin x, 21 = T, 1-, 1-sin x, dx, 1-sin x, 21 = T, mo1, 1-sin x, 1-, cos x, 21 = T, dx, 1, 1-, cos?, sin x, dx, cos²,, 21 = T, 21 = (1-sec² x+secx tan x) dx, 21 = r[x- tan x+ sec x], 21 = T(T-, a)-(0-tan 0+sec0)], TT - tan t + sec t, 21-지 [x-0-1-0-1]=x (x-2), -2), - Tt, f de, Ex. (3), x+x, $ 25-x, Solution : 1=f, x+x?, I=25-x, dx +, -325-x², dx ..(1), -3 25-x², 69

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Let f(x) =, 25-x, f(-x) =-, 25-(-x), -=-f(x), 25-x2, . f(x) is an odd function., -dx D0, ..(2), 25- х*, Let g(x) = 25-, – x?, (-x)*, 25-(-x) 25-x, g(-x) =, = g(x), .g(x) is an even function., x², dx =, 25- x, dx .(3), Jo 25-x, द, From (1), (2) and (3) we get,, dx, I=2), 25-x, = 2[ 25– 25 + x*, 25-(25-x), 25-х, dx, 25- x2, = 2f;, 25, -1 dx, 25 - x2, 25, -log, =2, 2(5), 5+x, 5-x, 5+3, 5+0, 0-, 5-0, = 2, log, .3, 5-3, 8., = 2, log, 3--log(1), 2, = 2 log (4)-3, = 5 log 4-6, :L*** 5 log 4-6, x+x?, dx =, 25 - x2, 70