CBSE  /  Class 12  /  Maths  /  Integrals

  • 1. 
    ∫x² sin x³ dx =

  • \(\frac{1}{3}\) cos x³ + c
  • –\(\frac{1}{3}\) cos x + c
  • \(\frac{-1}{3}\) cos x³ + c
  • \(\frac{1}{2}\) sin² x³ + c

  • 2. 
    ∫\(\frac{cos 2x- cos 2θ}{cos x – cos θ}\)dx is equal to

  • 2 (sin x + x cos θ) + C
  • 2 (sin x – x cos θ) + C
  • 2 (sin x + 2x cos θ) + C
  • 2 (sin x – 2x cos θ) + C

  • 3. 
    ∫\(\frac{dx}{sin(x-a)sin(x-b)}\) is equal to

  • sin(b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C
  • cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-b)}\)| + C
  • cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C
  • sin (b – a) log |\(\frac{sin (x-a)}{sin(x-b)}\)| + C

  • 4. 
    ∫tan √xdx is equal to

  • (x + 1)tan √x – √x + C
  • x tan √x – √x + C
  • √x – x tan √x + C
  • √x – (x + 1)tan √x + C

  • 5. 
    ∫e(\(\frac{1-x}{1+x^2}\))² dx is equal to

  • \(\frac{e^x}{1+x^2}\) + C
  • –\(\frac{-e^x}{1+x^2}\) + C
  • \(\frac{e^x}{(1+x^2)^2}\) + C
  • \(\frac{-e^x}{(1+x^2)^2}\) + C

  • 6. 
    If ∫\(\frac{dx}{(x+2)(x^2+1)}\) = a log |1 + x²| + b tan x + \(\frac{1}{5}\) log |x + 2| + C, then

  • a = \(\frac{-1}{10}\), b = \(\frac{-2}{5}\)
  • a = \(\frac{1}{10}\), b = \(\frac{-2}{5}\)
  • a = \(\frac{-1}{10}\), b = \(\frac{2}{5}\)
  • a = \(\frac{1}{10}\), b = \(\frac{2}{5}\)

  • 7. 
    ∫ \(\frac{x^3}{x+1}\) is equal to

  • x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 – x| + C
  • x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 – x| + C
  • x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 + x| + C
  • x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 + x| + C

  • 8. 
    If ∫\(\frac{x^3dx}{\sqrt{1+x^2}}\) = a(1 + x²)+ b\(\sqrt{1 + x^2}\) + C, then

  • a = \(\frac{1}{3}\), b = 1
  • a = \(\frac{-1}{3}\), b = 1
  • a = \(\frac{-1}{3}\), b = -1
  • a = \(\frac{1}{3}\), b = -1

  • 9. 
    \(\int_{-\pi / 4}^{\pi / 4}\) \(\frac{dx}{1+cos 2x}\) dx is equal to

  • 1
  • 2
  • 3
  • 4

  • 10. 
    \(\int_{0}^{\pi / 2}\) \(\sqrt{1+sin 2x}\) dx is equal to

  • 2√2
  • 2(√2 + 1)
  • 0
  • 2(√2 – 1)
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