Title CBSE - MATHEMATICS (PART - II).pdf ✅

2 E (viii) d dx (sin x) = cos x cos x dx sin x C    (ix) d dx (tan x) = sec2 x 2 sec x dx tan x C    (x) d dx (–cot x) = cosec2 x 2 cosec x dx cot x C     (xi) d dx (sec x) = sec x tan x sec x tan x dx sec x C    (xii) d dx (–cosec x) = cosec x cot x cosecx cot x dx cosecx C     (xiii) d dx (sin–1 x) = 2 1 1 x  1 2 1 dx sin x C 1 x      (xiv) d dx (–cos –1 x) = 2 1 1 x  1 2 1 dx cos x C 1 x       (xv) d dx (tan–1 x) = 2 1 1 x  1 2 1 dx tan x C 1 x      (xvi) d dx (–cot–1 x) = 2 1 1 x  1 2 1 dx cot x C 1 x       (xvii) d dx (sec–1 x) = 2 1 x x 1 1 2 1 dx sec x C x x 1      (xviii) d dx (–cosec –1 x) = 2 1 x x 1 1 2 1 dx cosec x C x x 1       4. BASIC THEOREMS ON INTEGRATION : If f(x), g(x) are two functions of a variable x and k is a constant, then (i) k f (x)dx k f (x)dx    (ii) [f (x) g(x)]dx f (x)dx g(x)dx       (iii) d dx   f (x)dx f (x)   (iv) d f(x) dx f(x) dx         + C (v) If f x   dx = (x) + C, then f ax b     dx = 1 a (ax + b) + C   d 1 (ax b) '(ax b) f (ax b) dx a             