Can I print a image larger than 4x6 directly from iPad's photo application to a HP Air Print printer without a additional app?

You can copy and paste the image onto a blank Pages document. Then print letter-sized.

That is, you can copy a jpg from iPhoto and play with the size & format after dropping it on the Pages blank page.

The short answer is No.

Air print is very limited regarding the size of photos you can print. However, if you get the HP printing app from the app store (free), the app will allow you to choose different sizes of photos you wish to print. I have found this is the only way to change photo size during printing using the iPad.

jerryone1942 wrote:

Can I print a image larger than 4x6 directly from iPad's photo application to a HP Air Print printer without a additional app?

It depends upon the capabilities of your printer. If you have an HP printer with a photo tray then the Photo app will print to whatever size you load in to that tray.

There's some more information here:

Using AirPrint to Print Various Photo Sizes

With other printers the user is given a choice from the printer's loaded paper sizes. You can see an example of that here:

The Many Faces of the iOS Print Panel