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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Indefinite Integration

JEE Main · Mathematics · Indefinite Integration

If ∫ f (x)cos xdx = (1)/(2)\ f(x)\ 2 + c, then f( x) is

If ∫f∫ f\left(x\right)cos xdx = 12{f(x)}\dfrac{1}{2}\left\{f\left(x\right)\right\}2+c,2 + c, then f\left(x\right) is

Options

  1. Ax+cx + c
  2. Bsinx+csin x + c
  3. Ccosx+ccos x + c
  4. Dcc

Correct answer

B. sinx+csin x + c

Step-by-step solution

Given,& ∫f(x)cosxdx=12{f(x)}2+c∫ f\left(x\right)cos xdx = \dfrac{1}{2}\left\{f\left(x\right)\right\}2 + c

Differentiate both sides we get,~

f(x)cosx=12⋅2f(x)f′(x)f\left(x\right)cos x = \dfrac{1}{2} ⋅ 2f\left(x\right)f^{′} ( x )

Then, f′(x)=cosxf^{′}\left(x\right) = cos x

Integrate both the sides we get,~

f(x)=sinx+cf\left(x\right) = sin x + c

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