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AP EAMCET202017 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual

If ( (13 x)- (14 x) 1+2 (9 x) d x= (4 x) a - (5 x) b ) (+c ), then (a^b= )

Options

  1. A(4^5 )
  2. B(5^4 )
  3. C(4^4 )
  4. D(5^5 )

Correct answer

A. (4^5 )

Step-by-step solution

Given, (I= 13 x- 14 x 1+2 9 x d x ) Let, ( aligned f(x) & = 13 x- 14 x 1+2 9 x & = 9 x( 13 x- 14 x) 9 x+ 18 x & = 9 x-2 27 2 x (- x 2 ) 2 27 x 2 (- 9 x 2 ) & = 9 x x 2 ( 9 x 2 ) =2 9 x 2 x 2 & = ( 9 x 2 - x 2 )- ( 9 x 2 + x 2 ) & = 4 x- 5 x aligned ) So, ( aligned I & = ( 4 x- 5 x) d x & = 4 x 4 - 5 x 5 +C aligned ) Hence, (a^b=4^5 )

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