How to permanently uninstall Dropbox

Just hold your finger down on the app icon untii it starts to wiggle, then tap it to delete.

Single tap the home button to exit the mode. I do know that your dropbox account will remain open for several months or more. They will notify you when they are ready to purge it.

or you can look into signing out and deleting your account, but I never explored that, I just waited until they purged it.

If you have restrictions enabled on your iPad, you may be prohibited from deleting apps. To disable that you'd need to sign into the restrictions and disable the prohibition on deleting apps.

Tap and hold on the DropBox icon until it starts to wiggle. Tap the little black "x" that appears on the icon. Confirm the deletion.