यदि f(x) = sech x है तो इसका समाकलन क्या है?

  1. log (cosh x) + C
  2. tan-1 (sin h x) + C
  3. 2 tanh-1 ex + C
  4. sinh x (½ (ex – e-x)) + C

Answer (Detailed Solution Below)

Option 2 : tan-1 (sin h x) + C
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Detailed Solution

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दिया गया है कि, f(x) = sech x,

समाकलन,

⇒ Substitute u = sinh x

du = cosh x dx

 

⇒ substitute u = tan θ

du = sec2θ dθ

= θ + c

= tan-1(u) + c

= tan-1 (sin hx) + c

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