₀^ 4 x+ x 9+16 2 x d x=k 3 , then k=

Step-by-step solution

Let I= ₀^ 4 x+ x 9+16 2 x d x=K 3 Put x- x=t ( x+ x) d x=d t ...(1) Now squaring equation (1), we get aligned I &= _ -1 ⁰ d t 9+16 (1-t² ) &= _ -1 ⁰ d t 25-16 t² = 1 16 _ -1 ⁰ d t ( 5 4 )²-t² aligned array l = 1 16 1 2 ( 5 4 ) [ 5 4 +t 5 4 -t ]_ -1 ⁰= 1 40 [ ( 5+4 t 5-4 t ) ]_ -1 ⁰= 1 40 [ (1)- ( 1 9 ) ] = 1 40 ( 9)= 1 40 3²= 2 40 3= 1 20 3 array As per given data, K= 1 20