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Calculate a numerical integral with enough precision

• To: mathgroup at smc.vnet.net
• Subject: [mg114668] Calculate a numerical integral with enough precision
• From: alphatest <iliurarfwpuap at mailinator.com>
• Date: Sun, 12 Dec 2010 05:45:17 -0500 (EST)

How can we calculate the following integral up to 10-12 decimal places?

integrate exp(sin(1/x)) , x=0..pi/2

It's as if no integration method or precision option lets you calculate more than 5-6 decimal places. Is it possible?