(Adds analyst's view on EPS, updates stock)

By Noel Randewich

SAN FRANCISCO, June 12 (Reuters) - Chipmaker Intel Corp on Thursday raised its outlook for the second quarter and the full year, citing stronger-than-expected demand for personal computers used by businesses.

Shares of Intel jumped more than 4 percent in extended trade as the chipmaker's improved forecast lifted hopes for a PC industry that been shrinking due to consumers' preferences for tablets and smartphones.

Intel said it now expects second-quarter revenue of $13.7 billion, plus or minus $300 million. Intel had previously forecast revenue of $13 billion, plus or minus $500 million.

The chipmaker said it expects "some" revenue growth for the full year, compared with its previous forecast of flat revenue.

The Santa Clara, California company also raised the mid-point of its gross margin forecast range for the second quarter, which ends at the end of June, by 1 point to 64 percent.

With personal computer shipments falling for eight straight quarters through March, some analysts have suggested the industry's decline is close to hitting bottom, potentially giving Intel breathing room as it struggles to develop better processors for mobile and wearable devices.

Demand from companies for PCs likely received a boost recently due to Microsoft's winding down of support in April for its Windows XP operating system, analysts say.

"PCs have been getting less bad for a while," said Bernstein analyst Stacy Rasgon. "But if it's all business PCs then the question is going to be sustainability."

Intel's revised revenue and gross margin forecasts for the June quarter could translate to earnings per share of 52 cents, RBC analyst Doug Freedman said in a note to clients.

For the second quarter, analysts on average had expected EPS of 47 cents and revenue of $13.02 billion, according to Thomson Reuters I/B/E/S.

Intel is expected to report its second-quarter results on July 15.

Shares of Intel jumped 4.97 percent in extended trade after closing up 0.11 percent at $27.96 on Nasdaq.

(Reporting by Noel Randewich; Editing by Cynthia Osterman)