| By Fairyofwind (Fairyofwind) on Thursday, August 14, 2003 - 10:19 pm: Edit |
Find the value of this definite integral:
Integral[Sin[x^2]/Sin[x],x,-1,1].
| By Jason817 (Jason817) on Thursday, August 14, 2003 - 10:43 pm: Edit |
is it .919??? My calc comes up with 0 but you're looking for the positive area of the shaded region.
| By Fairyofwind (Fairyofwind) on Thursday, August 14, 2003 - 10:44 pm: Edit |
No it's 0. But show it WITHOUT using your calculator!
| By Serene (Serene) on Thursday, August 14, 2003 - 10:47 pm: Edit |
Nice fairy! =)
One of our calc class tshirt designs (eventually rejected) was to have a really really complicated integral that go from -pi to +pi, just like that =)
| By Jason817 (Jason817) on Thursday, August 14, 2003 - 10:51 pm: Edit |
Well any definite integral like that involving a function with origin symmetry and boundries of -x and +x would end up being zero, will it not?
| By Fairyofwind (Fairyofwind) on Thursday, August 14, 2003 - 10:55 pm: Edit |
Hehehehe... good! But because of the way the improper integral is defined, an integral from say -2003 to 2003 of that is not 0, due to infinities where Sin[x]=0, but otherwise yes!
| By Serene (Serene) on Thursday, August 14, 2003 - 10:57 pm: Edit |
Jason: not all definite integrals. For example,
ò-x x 1/sin(x) dx will not get you 0 =) Gotta be careful!
Yeah. Fairy was careful to include sin(x^2), so there's a limit at x=0 =)
| By Jason817 (Jason817) on Thursday, August 14, 2003 - 11:02 pm: Edit |
Ah yes, good point.
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