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# Integral of (sin (x)) ^ (3/2) from 0 to pi?

 Posts: 1,518 Add as FriendChallenge to a DebateSend a Message 6/4/2013 11:33:01 PMPosted: 4 years agoI can't seem to figure out the Integral of (sin(x)) ^ (3/2) from 0 to pi, this is for calculous 2 level math. Thanx in advance.I cannot write in English, because of the treacherous spelling. When I am reading, I only hear it and am unable to remember what the written word looks like." "Albert Einstein http://www.twainquotes.com... , http://thewritecorner.wordpress.com... , http://www.onlinecollegecourses.com...
 Posts: 64 Add as FriendChallenge to a DebateSend a Message 6/4/2013 11:51:04 PMPosted: 4 years agoLOL it cannot be hand calculated. ^_^integrals.wolfram.com/index.jsp?expr=Sin[x]^%283%2F2%29&random=falseReturns an elliptic integral of the first kind, which cannot be expressed in terms of elementary functions. Rather, they are determined numerically.The definite integral from 0 to Pi gives2/3 Sqrt[2] EllipticK[1/2] ~ 1.74804You can try this command in Mathematica:Integrate[Sin[x]^(3/2), {x, 0, Pi}]NIntegrate[Sin[x]^(3/2), {x, 0, Pi}]I think you might have gotten the formula wrong :PIf you want, try to put Sin[x] = u and solve from there.
 Posts: 1,518 Add as FriendChallenge to a DebateSend a Message 6/5/2013 12:17:43 AMPosted: 4 years agoThe full problem reads "The region bounded by the x - axis and y = sin^(3/2)(x) (0
 Posts: 64 Add as FriendChallenge to a DebateSend a Message 6/5/2013 12:34:30 AMPosted: 4 years agoWell, the area caused by the rotating function is Pi*(y^2) -> so you would have to find the integral of [(sin (x) )^(3/2)]^2 = Sin^3(x), from 0 to piThis is *much* easier than the formal problem
 Posts: 11,204 Add as FriendChallenge to a DebateSend a Message 6/5/2013 12:52:40 AMPosted: 4 years agoAt 6/5/2013 12:34:30 AM, hereiam2005 wrote:Well, the area caused by the rotating function is Pi*(y^2) -> so you would have to find the integral of [(sin (x) )^(3/2)]^2 = Sin^3(x), from 0 to piThis is *much* easier than the formal problemyou can just do an integration tablehttp://integral-table.com...Open borders debate: http://www.debate.org...
 Posts: 1,518 Add as FriendChallenge to a DebateSend a Message 6/5/2013 12:54:37 AMPosted: 4 years agoAt 6/5/2013 12:34:30 AM, hereiam2005 wrote:Well, the area caused by the rotating function is Pi*(y^2) -> so you would have to find the integral of [(sin (x) )^(3/2)]^2 = Sin^3(x), from 0 to piThis is *much* easier than the formal problem*Feels stupid*, *Facepalms self*. Thanx.I wonder if this qualifies for the weekly stupid.I cannot write in English, because of the treacherous spelling. When I am reading, I only hear it and am unable to remember what the written word looks like." "Albert Einstein http://www.twainquotes.com... , http://thewritecorner.wordpress.com... , http://www.onlinecollegecourses.com...
 Posts: 64 Add as FriendChallenge to a DebateSend a Message 6/5/2013 1:07:47 AMPosted: 4 years agoAt 6/5/2013 12:54:37 AM, 1Devilsadvocate wrote:At 6/5/2013 12:34:30 AM, hereiam2005 wrote:Well, the area caused by the rotating function is Pi*(y^2) -> so you would have to find the integral of [(sin (x) )^(3/2)]^2 = Sin^3(x), from 0 to piThis is *much* easier than the formal problem*Feels stupid*, *Facepalms self*. Thanx.I wonder if this qualifies for the weekly stupid.LOL it was nothing
 Posts: 727 Add as FriendChallenge to a DebateSend a Message 6/26/2013 7:12:11 AMPosted: 4 years agoGo to wolframalpha for this stuff."Politics is supposed to be the second-oldest profession. I have come to realize that it bears a very close resemblance to the first." -Ronald Reagan "The notion of political correctness declares certain topics, certain expressions even certain gestures off-limits. What began as a crusade for civility has soured into a cause of conflict and even censorship." -George H.W. Bush
 Posts: 4,236 Add as FriendChallenge to a DebateSend a Message 6/26/2013 7:34:48 AMPosted: 4 years agoAt 6/26/2013 7:12:11 AM, tmar19652 wrote:Go to wolframalpha for this stuff.Yes. Definitely. Their Calc I app even shows how to do it.We are not dead. We have never lived. - Varg Vikernes, "Det som en gang var"
 Posts: 1 Add as FriendChallenge to a DebateSend a Message 10/19/2015 4:44:03 PMPosted: 2 years agoThe integral of sin(x/2) cos(x/3) from 0 to pi/2 is a number. If you "putd/dx in front of the integral" the answer is 0. Matlab is correct.On the other hand, for any function f(x),one version of the fundamental theorem of calculus saysInt[0,pi/2] d/dx f(x) dx = f(pi/2) - f(0)In this case, f(x) = sin(x/2) cos(x/3); f(0) = 0,f(pi/2) = sin(pi/4) cos(pi/6) ... tan(pi/4) = 1 so sin(pi/4) = cos(pi/4) = sqrt(2)/2cos (pi/6) = sqrt (1 - sin(pi/6)^2) = sqrt (3/4) = sqrt(3)/2f(pi/2) = sqrt(2) sqrt(3) /4 = sqrt (6) / 4http://www.downloadfreepdf.com...