Let the functions f:R→R and g:R→R be defined by f(x)=ex−1−e−|x−1| and g(x)=12ex−1+e1−x Then the area of the region in the first quadrant bounded by the curves y=f(x),y=g(x) and x=0 is

here,f(x)=0x≤1ex−1−e1−xx≥1&g(x)=12ex−1+e1−x solve f(x)&g(x) therefore ex-1-e1-x=12  ex-1+e1-x⇒e2x-2=3⇒x=1+ln3  So bounded area =∫01 12ex−1+e1−xdx+∫11+ln⁡3 12ex−1+e1−x−ex−1+e1−xdx=12ex−1−e1−x01+−12ex−1−32e1−x11+ln3=12e−1e+−32−32+2=2−3+12e−1e