19.3.30 Linear operators

condition: Find the operator conjugate to the operator \( A: L_{2}[0,1] \rightarrow L_{2}[0,1] \), if: a) \( A x(t)=\int_{0}^{t} x(s) d s \), b) \( A x(t)=t x(t) \) c) \( A x(t)=t \int_{0}^{1} x(s) d s \).