Show that

and

and

and finally

Show that the area enclosed by a curve defined through the equation

where

c is a positive odd integer and b is a positive even integer is

Come on people lets see that skill (Sun)

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- May 18th 2008, 08:58 PMMathstud28Three impossible integrals and two challenging ones
Show that

and

and

and finally

Show that the area enclosed by a curve defined through the equation

where

c is a positive odd integer and b is a positive even integer is

Come on people lets see that skill (Sun) - May 18th 2008, 10:02 PMNonCommAlg
well, they are actually pretty easy. i'll do the first three for now:

here we need to have then we have:

by Euler's Reflection formula

Quote:

Quote:

now, again, by Euler's Reflection formula: and

clearly put these two in to get the result. Q.E.D. - May 19th 2008, 06:09 AMKrizalid
See here.