CBSE  /  Class 12  /  Maths  /  Integrals

  • 1. 
    \(\int_{0}^{\pi^{2} / 4} \frac{\sin \sqrt{y}}{\sqrt{y}}\)

  • 1
  • 2
  • \(\frac{π}{4}\)
  • \(\frac{π^2}{8}\)

  • 2. 
    \(\int_{0}^{\infty} \frac{1}{1+e^{x}}\) dx =

  • log 2
  • -log 2
  • log 2 – 1
  • log 4 – 1

  • 3. 
    \(\int_{0}^{1}\) x(1 – x) is equal to

  • \(\frac{1}{10010}\)
  • \(\frac{1}{10100}\)
  • \(\frac{1}{1010}\)
  • \(\frac{11}{10100}\)

  • 4. 
    What is the value of \(\int_{0}^{1}\) \(\frac{d}{dx}\){sin(\(\frac{2x}{1+x^2}\))}dx?

  • 0
  • π
  • -π
  • \(\frac{π}{2}\)

  • 5. 
    \(\int_{0}^{1}\) \(\frac{x}{1+x}\) dx =

  • 1 – log 2
  • 2
  • 1 + log 2
  • log 2

  • 6. 
    ∫\(\frac{sin x + cos x}{\sqrt{1+2sin x}}\) dx =

  • log(sin x – cos x)
  • x
  • log x
  • log sin (cos x)

  • 7. 
    ∫log xdx =

  • log 10.x log(\(\frac{x}{e}\)) + c
  • log e.x log(\(\frac{x}{e}\)) + c
  • (x – 1) log x + c
  • \(\frac{1}{x}\) + c

  • 8. 
    ∫(\(\frac{cos 2θ – 1}{cos 2θ + 1}\)) dθ =

  • tan θ – θ + c
  • θ + tan θ + c
  • θ – tan θ + c
  • -θ – cot θ + c

  • 9. 
    ∫\(\frac{2dx}{\sqrt{1-4x^2}}\) =

  • tan (2x) + c
  • cot (2x) + c
  • cos(2x) + c
  • sin(2x) + c

  • 10. 
    Value of ∫\(\frac{dx}{\sqrt{2x – x^2}}\)

  • sin(x – 1) + c
  • sin(1 + x) + c
  • sin(1 + x²) + c
  • –\(\sqrt{2x-x^2}\) + c
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