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)

Printable View

- May 18th 2008, 09:58 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, 11:02 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, 07:09 AMKrizalid
See here.