CBSE  /  Class 12  /  Maths  /  Integrals

  • 1. 
    \(\int \frac{x+\sin x}{1+\cos x}\) dx is equal to

  • log |1 + cos x | + c
  • log | x + sin x | + c
  • x – tan + c
  • x. tan \(\frac{x}{2}\) + c

  • 2. 
    ∫1.dx =

  • x + k
  • 1 + k
  • \(\frac{x^2}{2}\) + k
  • log x + k

  • 3. 
    ∫\(\frac{dx}{√x}\) =

  • √x + k
  • 2√x + k
  • x + k
  • \(\frac{2}{3}\)x + k

  • 4. 
    ∫\(\frac{dx}{1+cos x}\) =

  • tan \(\frac{x}{2}\) + k
  • \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
  • 2 tan \(\frac{x}{2}\) + k
  • tan² \(\frac{x}{2}\) + k

  • 5. 
    \(\int_{a}^{b}\) x dx =

  • tan \(\frac{x}{2}\) + k
  • \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
  • 2 tan \(\frac{x}{2}\) + k
  • tan² \(\frac{x}{2}\) + k

  • 6. 
    If x > a, ∫\(\frac{dx}{x^2-a^2}\) =

  • \(\frac{2}{2a}\) log \(\frac{x-a}{x+a}\) + k
  • \(\frac{2}{2a}\) log \(\frac{x+a}{x-a}\) + k
  • \(\frac{1}{a}\) log(x² – a²) + k
  • log(x + \(\sqrt{x^2-a^2}\) + k)

  • 7. 
    ∫\(\frac{cos 2x dx}{(sinx+cosx)^2}\) =

  • –\(\frac{1}{sinx+cosx}\) + c
  • log | sin x + cos x | + c
  • log | sin x – cos x | + c
  • \(\frac{1}{(sinx+cosx)^2}\)

  • 8. 
    ∫\(\frac{(1+logx)^2}{1+x^2}\) dx =

  • \(\frac{1}{3}\)(1+log)³ + c
  • \(\frac{1}{2}\)(1+log)² + c
  • log (log 1 + x) + 2
  • None of these

  • 9. 
    \(\int_{0}^{1}\frac{(tan^{-1}x)^2}{1+x^2}\) dx =

  • 1
  • \(\frac{π^2}{64}\)
  • \(\frac{π^2}{192}\)
  • None of these

  • 10. 
    \(\int_{-2}^{2}\) |x|dx =

  • 0
  • 2
  • 1
  • 4
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