Q30 / 50 · Manipal (MET) 2023 · Mathematics

$\int f(x) d x=g(x)$, then $\int \cos x f(\sin x) d x$ is equal to

  • A
    $g(\cos x)+C$
  • Correct answer
    B
    $g(\sin x)+C$
  • C
    $\int g(x)+\sin x+C$
  • D
    $f(\sin x)+g(\cos x)+C$

Solution

Here, $\int f(x) d x=g(x)$ Now, $\int \cos x f(\sin x) d x$ Let, $\sin x=k \Rightarrow \cos x d x=d k$ $\therefore \int f(k) d k=g(k)+C=g(\sin x)+C$

Hence, the correct answer is option: 'B'.

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