C cyndix3 New Member Joined Jan 21, 2011 Messages 7 Gender Female HSC 2014 Jan 21, 2011 #1 Hi, Hope you guys can help me! Im having difficulties integrating this trig function: sin3xcos2x Thanx heaps in advanced!
Hi, Hope you guys can help me! Im having difficulties integrating this trig function: sin3xcos2x Thanx heaps in advanced!
B Bored Of Fail 2 Banned Joined Jan 13, 2011 Messages 354 Gender Male HSC N/A Jan 21, 2011 #2 use so called product to sum formula sin(A+B ) + sin(A-B) = sinAcosB + cosAsinB + sinAcosB -cosAsinB = 2 sinAcosB therefore sinAcosB = (1/2) ( sin(A+B) + sin(A-B) ) so set A=3x , B=2x we want the integral (1/2) ( sin(5x) + sin(x) ) we want (1/2) integral ( sin(5x) -sin(x) ) dx = (1/2) ( (-1/5) cos(5x) -cos(x) ) +C Last edited: Jan 21, 2011
use so called product to sum formula sin(A+B ) + sin(A-B) = sinAcosB + cosAsinB + sinAcosB -cosAsinB = 2 sinAcosB therefore sinAcosB = (1/2) ( sin(A+B) + sin(A-B) ) so set A=3x , B=2x we want the integral (1/2) ( sin(5x) + sin(x) ) we want (1/2) integral ( sin(5x) -sin(x) ) dx = (1/2) ( (-1/5) cos(5x) -cos(x) ) +C
B Bored Of Fail 2 Banned Joined Jan 13, 2011 Messages 354 Gender Male HSC N/A Jan 21, 2011 #3 The product to sum formulas can be derived relatively easily, and you can find them all on wikipedia, remember the derivations though, not the formula itself
The product to sum formulas can be derived relatively easily, and you can find them all on wikipedia, remember the derivations though, not the formula itself
