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AP EAMCET202317 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If f(x) d x= (x) , then x^5 f (x^3 ) d x=

Options

  1. A1 3 [x^3 (x^3 ) ]- x^2 (x^3 ) d x
  2. B1 3 [x^3 (x^3 ) ]+ x^2 (x^3 ) d x
  3. C- 1 3 [x^3 (x^3 ) ]- x^3 (x^3 ) d x
  4. D- 1 3 [x^3 (x^3 ) ]+ x^3 (x^3 ) d x

Correct answer

A. 1 3 [x^3 (x^3 ) ]- x^2 (x^3 ) d x

Step-by-step solution

f( x ) dx = ( x ) Let I = x^5 f (x^3 ) d x= x^3 f (x^3 ) x^2 d x Let x^3=t 3 x^2 d x=d t x^2 d x= d t 3 I = t f( t ) d t 3 = 1 3 t f(t) dt = 1 3 [t f(t) d t-1 f(t) d t ] aligned & = 1 3 [t (t)- (t) d t ]+c & = 1 3 x^3 (x^3 )- 1 3 (x^3 ) 3 x^2 d x & = 1 3 x^3 (x^3 )- x^2 (x^3 ) d x aligned

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