Latitude 7940 Swollen battery

It's good that you caught it.  A swelling battery can damage components such as touchpad and keyboard.

Please do not throw it in the garbage. Take it somewhere that it will be properly disposed of. In many places, stores such as Best Buy and Staples will accept old "tech" for proper disposal/recycling. A recycling depot may also accept batteries.

These links should be helpful to you:

Swollen Battery Information and Guidance | Dell Canada

How Do I Recycle or Dispose of My Dell Battery | Dell US

And if you want a replacement, you may buy a genuine Dell battery direct from Dell or from Parts-People. (Each of those links goes directly to the batteries for Latitude 7490. As I cannot find a Latitude 7940, I guessed that you might mean Latitude 7490 if you transposed two digits.)

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.)