The value of the integral - ² x 1+ a ^ x d x , where a >0 , is -

Step-by-step solution

array l I= _ - ^ ² x 1+a^ x d x (1) _ a ^ b f(x) d x= _ a ^ b f(a+b-x) d x I= _ - ^ ²(-x) 1+a^ -x d x I= _ - ^ a^ x ² x 1+a^ x d x . . (2) array add equation (1) and (2) 2 I = _ - ^ ² x ( 1 1+ a ^ x + a ^ x 1+ a ^ x ) dx I = ₀^ ² x d x =2 ₀^ / 2 ² x dx = / 2