Class XII

∫ √a2−x2 dx is equal to
  1. [(x/2) √a²−x²)]−[(a²/2) sin⁻¹(x/a)]+C
  2. [(x/2) √a²−x²)] + [(a²/2) sin⁻¹(x/a)]+C
  3. [(x/2) √a²−x²)] + [(a²/2) log x √a²−x² ]+ C
  4. [(a/2) √a²−x²)] + [(x²/2) log x √a²−x²] + C
∫(x cos x)/√( x sin x + cos x ) dx is equal to
  1. (3/5)( x cos x − sin x)³ ⁄ ² + C
  2. (1/2)( x sin x − cos x)¹ ⁄ ² + C
  3. 2( x sin x + cos x)¹ ⁄ ² + C
  4. (2/3)( x sin x + cos x)³ ⁄ ² + C
If ∫f(x) f x dx = g (x) + C and also ∫f(x) f x dx = h(x) + D, then
  1. g (x) . h (x) = constant
  2. g(x)/h(x)=constant
  3. g (x) - h (x) = constant
  4. h (x) + g (x) = constant
∫(tan x+cot x) dx is equal to
  1. log | sin x + cos x|+C
  2. log | cot x|+C
  3. log | tan x|+C
  4. None of these
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