Hi, Can someone please show me how to solve this, step by step? Integrate the following: sinxcosxcos2x Apparently the answer is 1/8(sin2x)^2 + C Does sinxcosx go outside of the integrand as a factor?
Follow Math Help Forum on Facebook and Google+
Originally Posted by CSG18 Hi, Can someone please show me how to solve this, step by step? Integrate the following: sinxcosxcos2x Apparently the answer is 1/8(sin2x)^2 + C Does sinxcosx go outside of the integrand as a factor? only constants can be factored out of an integral ... you know that. substitution ... let
Originally Posted by skeeter substitution ... let Sorry I do not understand what you did... How did it turn into ? I understand where the fraction came from though.
Originally Posted by CSG18 Sorry I do not understand what you did... How did it turn into ? I understand where the fraction came from though. Because If you dont know this, you need to look back at the topic double angle formula. Here it is: Double Angle The fraction is there because skeeter multiplied the term by , which is equal to 1
Originally Posted by CSG18 Hi, Can someone please show me how to solve this, step by step? Integrate the following: sinxcosxcos2x Apparently the answer is 1/8(sin2x)^2 + C Does sinxcosx go outside of the integrand as a factor? A function of the variabel NEVER "goes outside the integrand"! Only constants (with respect to the variable of integration) can be moved like that. Skeeter used the trig identity that sin(2x)= 2sin(x)cos(x) so that sin(x)cos(x)= (1/2)sin(2x).
Originally Posted by HallsofIvy A function of the variabel NEVER "goes outside the integrand"! Only constants (with respect to the variable of integration) can be moved like that. So why is it when you integrate 4cosx sin^3x dx, 4 cosx goes outside as a factor?
Originally Posted by CSG18 So why is it when you integrate 4cosx sin^3x dx, 4 cosx goes outside as a factor? No because is not a constant. 4 can go out of the integrand but this is not the optimal way to solve it If you use skeeter's hint of then Therefore Note that I have taken a factor of 1/2 out of the integral - this is because 1/2 is a constant
View Tag Cloud