19.2.1.2 Properties of normed spaces

Problem: Will the functions \[ \|\mathrm{x}\|_{1}=\int_{0}^{1}|x(t)| d t \text { and }\|x\|_{2}=\int_{0}^{1} e^{t}|x(t)| d t \] be norms on the space \( C([0,1]) \) ? If yes, will these norms be equivalent on the given space?