₂^ e [ 1 x - 1 ( x)^2 ] d x=a+ b 2 , then

Step-by-step solution

a + b 2 = ₂^ e [ 1 x - 1 ( x)^2 ] dx Put x = t 1 x dx = dt dx = e ^ t dt When x = e , t =1 and when x =2, t = 2 aligned & a+ b 2 = _ 2 ^1 ( 1 t - 1 t^2 ) e^t d t= [e^t 1 t ]_ 2 ^1=e- e^ 2 2 =e- 2 2 & a=e, b=-2 aligned