Question

If $\int \operatorname { cosec }$2x dx = ƒ (g(x)) + c, then –

• A. Range g(x) = (–, )
• B. Dom ƒ(x) = (–, )
• C. g (x) = sec² x
• D. ƒ¢(x) = 1/x for all x Ī (0, )

Answer 1

Answer: (A)

Range g(x) = (–, )

Answer 2

$\int \operatorname { cosec }$2x dx = ƒ (g(x)) + c

Ž cosec 2x = ƒ¢(g(x)) g¢(x)

Ž $\frac { 1 } { 2 \tan x }$ × sec² x = ƒ¢ (g(x)) g¢(x)

\ Ž ƒ(x) = $\frac{1}{2x}$, g¢(x) = sec² x

Dom. ƒ(x) = (–, ) – {0}, g (x) = tan x + c

Range g(x) = (–, ).