CBSE  /  Class 12  /  Maths  /  Integrals

  • 1. 
    Evaluate: ∫(2 tan x – 3 cot x)² dx

  • -4tan x – cot x – 25x + C
  • 4 tan x – 9 cot x – 25x + C
  • – 4 tan x + 9 cot x + 25x + C
  • 4 tan x + 9 cot x + 25x + C

  • 2. 
    Evaluate: ∫ sec²(7 – 4x)dx

  • –\(\frac{1}{4}\) tan(7 – 4x) + C
  • \(\frac{1}{4}\) tan(7 – 4x) + C
  • \(\frac{1}{4}\) tan(7 + 4x) + C
  • –\(\frac{1}{4}\) tan(7x – 4) + C

  • 3. 
    ∫ \(\frac{10x^9+10^xlog_e 10}{10^x+x^{10}}\) dx is equal to

  • 10 – x + C
  • 10+ x+ C
  • (10– x)+ C
  • log (10+ x) + C

  • 4. 
    Evaluate: ∫ sec x cosec xdx

  • \(\frac{3}{5}\) tan x – 3 tan x + C
  • –\(\frac{3}{5}\) tan x + 3 tan + C
  • –\(\frac{3}{5}\) tan x – 3 tan + C
  • None of these

  • 5. 
    ∫ \(\frac{a}{(1+x^2)tan^{-1}x}\) dx =

  • a log |tan x| + C
  • \(\frac{1}{2}\)(tanx)² + C
  • a log (1 + x) + C
  • None of these

  • 6. 
    ∫ \(\frac{cot x}{\sqrt[3]{sin x}}\) dx =

  • \(\frac{-3}{\sqrt[3]{sin x}}\) + C
  • \(\frac{-2}{sin^3 x}\) + C
  • \(\frac{3}{sin^{1/3}x}\) + C
  • None of these

  • 7. 
    Evaluate: ∫ \(\frac{1}{1+3sin^2x+8cos^2x}\) dx

  • \(\frac{1}{6}\) tan(2 tan x) + C
  • tan(2 tan x) + C
  • \(\frac{1}{6}\) tan(\(\frac{2 tan x}{3}\)) + C
  • None of these

  • 8. 
    Evaluate: ∫ \(\frac{1}{\sqrt{9+8x-x^2}}\) dx

  • -sin(\(\frac{x-4}{5}\)) + C
  • sin(\(\frac{x+4}{5}\)) + C
  • sin
  • None of these

  • 9. 
    ∫ \(\frac{dx}{1-cosx-sinx}\) is equal to

  • log |1 + cot\(\frac{x}{2}\)| + C
  • log |1 – tan\(\frac{x}{2}\)| + C
  • log |1 – cot\(\frac{x}{2}\)| + C
  • log |1 + tan\(\frac{x}{2}\)| + C

  • 10. 
    Evaluate: ∫ \(\frac{1}{\sqrt{1-e^{2x}}}\) dx

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