The problem statement has been attached. To show that T : V →R is a linear function It must satisfy 2 conditions: 1) T(cv) = cT(v) where c is a constant and 2) T(u+v) = T(u)+T(v) For condition 1) T(cv)=∫cvdx from 0 to 1 (I don't know how to put limits into the integral. cT(v)=c∫vdx (pulling a constant out of an integral) cT(v)=cT(v) I think I did the work for condition 1 right? For condition 2) T(u+v) where u=u1 and v=v1 T(u+v)=∫(u+v)dx T(u+v)=∫(u)dx + ∫(v)dx (this is called the sum rule of integration, I think). T(u+v)=T(u)+T(v) Did i do this right?