GATE 2013 MA Calculus

Question

Answer 1

let x+t=u

du = dt

i.e; limit changes to x+3 and x+1 with respective u

therefore integration becomes g(x)=F(x+3)-F(x+1) (F intergal of f)

g'(x)=f(x+3).(d/dx(x+3)) - f(x+1).(d/dx(x+1))

g'(x)=f(x+3).1-f(x+1).1

g'(0)=f(3)-f(1)

g'(0)=11-5

g'(0)=6