package java9;

import java.awt.BorderLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.*;
import javax.xml.bind.Marshaller.Listener;

public class Example7 extends JFrame implements ActionListener{
      JCheckBox JC1;
      JCheckBox JC2;
      JCheckBox JC3;
      JTextArea JT1;

      Example7()
      {
          this.setSize(300, 300);
          this.setTitle("我的窗体");
          //添加复选框
          JCheckBox JC1= new JCheckBox("艺术");   
          JCheckBox JC2= new JCheckBox("跳舞");   
          JCheckBox JC3= new JCheckBox("画画");
          //创建面板
          JPanel P1=new JPanel();
          JPanel P3=new JPanel();
          JT1=new JTextArea(1,1);
   
          //讲复选框，单选按钮加入面板
          P1.add(JC1);
          P1.add(JC2);
          P1.add(JC3);
          P3.add(JT1);
   
          //
          //将面板,文本域加入窗体
          this.add(P1,BorderLayout.NORTH);      
         
          this.add(P3,BorderLayout.SOUTH);        
          JC1.addActionListener(this);
          JC2.addActionListener (this);
          JC3.addActionListener(this);
          this.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
          this.setVisible(true);}                          
         public void actionPerformed(ActionEvent e) {
                String a="";
            if(JC1.isSelected())
            {
                a+="艺术";               
            }
            if(JC2.isSelected())
            {
                a+="跳舞";               
            }
            if(JC3.isSelected())
            {
                a+="画画";               
            }
            JT1.setText("我喜欢的活动："+a+"\n");
        }   

      public static void main(String[] args) {
        new Example7();
        }
}

46行

jcheckbox监听事件好像是addItemListener

好的我我试试