Faraday’s law in integral form is  (The symbols have their usual meaning)

\( E . ds = \frac {Q}{ε_0} \) \( \int E . dl=\frac{-d \phi}{d t} \) \( \int B . ds=0 \) \( \int B . dl=\mu_0\left(i_c+\varepsilon_0 \frac{d \phi}{d t}\right) \)

\( \int E . dl=\frac{-d \phi}{d t} \)

According to Faraday Law Induced emf $\varepsilon=-\frac{d \phi}{dt}$ And $\varepsilon=\int \vec{E} . \vec {dl}$  $\Rightarrow \int E . dl=-\frac{d \phi}{dt}$