AP EAMCET202018 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual
( ₀^ / 4 d x ^3(x) 2 (2 x) = )
Options
- A( 6 5 )
- B( 3 5 )
- C( 4 5 )
- D( 8 5 )
Correct answer
A. ( 6 5 )
Step-by-step solution
( aligned I & = ₀^ / 4 d x ^3 x 2 2 x = ₀^ / 4 d x ^3 x 4 x x & = ₀^ / 4 d x 2 ^4 x x = 1 2 ₀^ / 4 ^2 x (1+ ^2 x ) x d x aligned ) Let, ( x=t^2 ), then at (x=0, t=0 ) and at (x= 4 , t=1 and ^2 x d x=2 t dt ) ( aligned So, I & = ₀^1 (1+t^4 ) t d t t = ₀^1 (1+t^4 ) d t & = [t+ t^5 5 ]₀^1=1+ 1 5 = 6 5 aligned )