CBSE  /  Class 12  /  Maths  /  Integrals

  • 1. 
    ∫\(\frac{x^4+1}{x^2+1}\) dx is equal to

  • \(\frac{x^3}{3}\) + x + tan x + c
  • \(\frac{x^3}{3}\) – x + tan x + c
  • \(\frac{x^3}{3}\) + x + 2tan x + c
  • \(\frac{x^3}{3}\) – x + 2tan x + c

  • 2. 
    ∫(√x + \(\frac{1}{√x}\)) dx =

  • \(\frac{1}{x}\) x+ 2x+ c
  • \(\frac{2}{3}\) x+ \(\frac{1}{2}\)x+ c
  • \(\frac{2}{3}\) x+ 2x+ c
  • \(\frac{3}{2}\) x+ \(\frac{1}{2}\)x+ c

  • 3. 
    ∫\(\frac{sin^2x-cos^2x}{sin^2xcos^2x}\) dx is equal to

  • tan x + cos x + c
  • tan x + cosec x + c
  • tan x + cot x + c
  • tan x+ sec x + c

  • 4. 
    \(\frac{d}{dx}\)∫f(x)dx is equal to

  • f'(x)
  • f(x)
  • f'(x’)
  • f(x) + c

  • 5. 
    What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{\sqrt{tan x}}{\sqrt{tan x}+\sqrt{cot x}}\) dx?

  • \(\frac{π}{2}\)
  • \(\frac{π}{4}\)
  • \(\frac{π}{8}\)
  • None of these

  • 6. 
    What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{sinx – cos x}{1+sin xcos x}\) dx?

  • 1
  • \(\frac{π}{2}\)
  • 0
  • –\(\frac{π}{2}\)

  • 7. 
    What is the value of \(\int_{\pi / 6}^{\pi / 3}\) \(\frac{dx}{sin2x}\)?

  • \(\frac{1}{2}\) log(-l)
  • log(- 1)
  • log 3
  • log √3

  • 8. 
    What is the value of \(\int_{-1}^{1}\) sin³ x cos² xdx?

  • 0
  • 1
  • \(\frac{1}{2}\)
  • 2

  • 9. 
    What is the value of \(\int_{1}^{e} \frac{1+\log x}{x}\) dx?

  • \(\frac{3}{2}\)
  • \(\frac{1}{2}\)
  • e
  • \(\frac{1}{e}\)

  • 10. 
    \(\int_{-\pi / 2}^{\pi / 2}\) sin xdx =

  • -1
  • 0
  • 1
  • None of these
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