The Federal Aviation Administration is investigating reports that a Trans World Airways jet crossed prohibited airspace near the Capitol after leaving National Airport yesterday, federal sources said.

The departing Boeing 727 bound for New York apparently failed to make a sharp turn to the northwest and crossed the southern tip of the prohibited area for about five-eighths of a mile near the Capitol, a source said.

Pilots are prohibited from entering airspace around the Capitol, the White House, the Mall and the Naval Observatory under security regulations put in place by President Roosevelt in 1941.

FAA spokesman Ed Pinto said the agency is investigating the incident, and that officials will examine radar maps of the flight, which took off from National Airport at 1:59 p.m.

The incident was brought to the FAA's attention by top officials of the National Transportation Safety Board, who were having lunch at a restaurant in Southwest when they spotted the 727.

The TWA pilot received permission from the National control tower to take off on Runway 36, the airport's main north-south runway, and to make a sharp turn to the right to follow the Anacostia River north as the plane gained altitude, according to a source.

"He didn't negotiate his turn soon enough," the source said. "It was inadvertent."

The 727 crossed the area south of Independence Avenue and the Capitol, the source said.

The route over the Anacostia, which caused controversy because of noise over Southwest Washington in the early 1980s when several airlines used it frequently, is approved by the FAA.

Most of the jets that used the route then were twin-engine DC-9s, while the one in yesterday's incident was a three-engine 727, which is larger and less maneuverable.

Pilots departing from National for the north sometimes use the route because it saves 10 minutes and 35 miles, but in 1981 the FAA persuaded airlines to reduce its use because of Southwest residents' complaints.

A pilot who enters the banned airspace, which extends to 18,000 feet, can be fined or suspended. The area is penetrated every few months, usually by private or business pilots, FAA officials said.