register_activation_hook in oop approach

It doesn’t really matter. If you simply must have it inside a class, I would use a constant and a static method.

// in the main plugin file
define( 'MYPLUGIN_FILE', __FILE__ );

// include another file with this class in
class MyPlugin {

    public static function init() {
        register_activation_hook( MYPLUGIN_FILE, array( 'MyPlugin', 'install' ));
    }

    public static function install() {
         echo "little lamb, who made thee? is it wordpress or is it me";
    }
}

// call the static method
MyPlugin::init();