My Math Forum Integral of sin(x)*cos(x)
 User Name Remember Me? Password

 Calculus Calculus Math Forum

 September 9th, 2017, 04:55 AM #1 Member   Joined: Sep 2013 Posts: 84 Thanks: 2 Integral of sin(x)*cos(x) Hello I don't understand why I get different results when I try to find that integral. If I choose f' as cos(x) and g as sin(x) then using the partial integration formula the result is (1/2)*sin^2(x). If I choose f' as sin(x) and g as cos(x), then the result is -(1/2)*cos^2(x). The two results are not equal, so something is wrong (the 2nd result is correct). Last edited by skipjack; September 9th, 2017 at 12:22 PM.
 September 9th, 2017, 06:06 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,331 Thanks: 2457 Math Focus: Mainly analysis and algebra Recall that $\sin^2 x + \cos^2 x = 1$ so the two results differ only by an additive constant. Thus they have the same derivative and are therefore both primitives of the same function (your integrand). Note that an easier way to get a (third different) result is to use $\sin 2x = 2\sin x \cos x$ to simplify the integrand before you integrate. Thanks from ricsi046
 September 9th, 2017, 06:45 AM #3 Member   Joined: Sep 2013 Posts: 84 Thanks: 2 oh,I see,thanks Thanks from v8archie

 Tags integral, sinxcosx

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Jhenrique Calculus 5 June 30th, 2015 03:45 PM gen_shao Calculus 2 July 31st, 2013 09:54 PM maximus101 Calculus 0 March 4th, 2011 01:31 AM xsw001 Real Analysis 1 October 29th, 2010 07:27 PM maximus101 Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top