CBSE  /  Class 12  /  Maths  /  Integrals

  • 1. 
    If ∫ \(\frac{3x+4}{x^3-2x-4}\) dx = log |x – 2| + k log f(x) + c, then

  • f(x) = |x² + 2x + 2|
  • f(x) = x² + 2x + 2
  • k = –\(\frac{1}{2}\)
  • All of these

  • 2. 
    Evaluate: ∫ \(\frac{1-cosx}{cosx(1+cosx)}\) dx

  • log|sec x + tan x| – 2 tan(x/2) + C
  • log|sec x – tan x| – 2 tan(x/2) + C
  • log|sec x + tan x| + 2 tan(x/2) + C
  • None of these

  • 3. 
    ∫ cos(log.x)dx is equal to

  • \(\frac{1}{2}\) x[cos (logx) + sin(log x)]
  • x[cos (log x) + sin(log x)]
  • \(\frac{1}{2}\) x[cos (log x) – sin(log x)]
  • x[cos (log x) – sin(log x)]

  • 4. 
    ∫ |x| dx is equal to

  • \(\frac{1}{2}\) x² + C
  • –\(\frac{x^2}{2}\) + C
  • x|x| + C
  • \(\frac{1}{2}\) x|x| + C

  • 5. 
    ∫ sin xdx is equal to

  • cos x + C
  • x sin x + \(\sqrt{1-x^2}\) + C
  • \(\frac{1}{\sqrt{1-x^2}}\) + C
  • x sin x – \(\sqrt{1-x^2}\) + C

  • 6. 
    ∫ cos (\(\frac{1}{x}\))dx equals

  • x sec x + log |x + \(\sqrt{x^2-1}\)| + C
  • x sec x – log |x + \(\sqrt{x^2-1}\)| + C
  • -x sec x – log |x + \(\sqrt{x^2-1}\)| + C
  • None of these
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