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The integral of ( \cos x \sin x ) can be computed using a trigonometric identity. We use the identity ( \sin(2x) = 2 \sin x \cos x ), which allows us to rewrite the integral as:
[ \int \cos x \sin x , dx = \frac{1}{2} \int \sin(2x) , dx. ]
Integrating ( \sin(2x) ) gives:
[ \frac{-1}{2} \cos(2x) + C, ]
thus the final result is:
[ \int \cos x \sin x , dx = \frac{-1}{4} \cos(2x) + C. ]
What else can I help you with?
What is 1-cosxsinx plus 1 plus cosxsinx?
2
How is Riemann- stieltjes integral a generalization of Riemann integral?
In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.
What are some sentences with the word integral?
Political parties are an integral part of democracy. Religion is an integral part of Saudi Arabia. Greed is an integral part of human psychology.
State the difference between particular solution and particular integral?
Particular integral is finding what the integral is for example the integral of 2x is x^2 + C. Finding the particular solution would be finding what C equals from the particular integral.
Why is a summation greater than an integral?
It's not. It depends on the method you use for summation whether summation > integral or integral > summation.
What is 1-cosxsinx plus 1 plus cosxsinx?
2
How do you prove that integral sinx plus cosxsinx-cosx plus 2 cos2xdx equals 3?
Without specifying the limits of integration, the integral will always include an arbitrary constant, and you'll never get a numerical value for it. So the statement is untrue on its face, hence unprovable. We'll have a look at the trig later.
Why does -2sinxcosx equal -sin2x?
-4
What is the value of x for which cosxsinx 0.5?
You know that cosπ/4 and sinπ/4 both equal 1/root2, so multiplying them gets 1/2.
What is the indefinite integral of 3sinx-5cosx?
8
Integral in tagalog?
Integral in Tagalog: mahalaga
How is Riemann- stieltjes integral a generalization of Riemann integral?
In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.
Sentence for integral?
Elections are integral to democracies.
What is the convulusion integral?
Do you mean the Convolution Integral?
How do you put the word integral in a sentence?
What is a integral
What is integral number?
non integral is type of numbers behaviour: i can say that set of numbers without any "holes inside" are integral and set of numbers with "holes inside are non integral. example : integral group "1..100" non integral group "1,4,8,67"
Integral of cosine squared x?
Integral of cos^2x=(1/2)(cosxsinx+x)+CHere is why:Here is one method: use integration by parts and let u=cosx and dv=cosxdxdu=-sinx v=sinxInt(udv)=uv-Int(vdu) so uv=cosx(sinx) and vdu=sinx(-sinx)so we have:Int(cos^2(x)=(cosx)(sinx)+Int(sin^2x)(the (-) became + because of the -sinx, so we add Int(vdu))Now it looks not better because we have sin^2x instead of cos^2x,but sin^2x=1-cos^2x since sin^2x+cos^2x=1So we haveInt(cos^2x)=cosxsinx+Int(1-cos^2x)=cosxsinx+Int(1)-Int(cos^2x)So now add the -Int(cos^2x) on the RHS to the one on the LHS2Int(cos^2x)=cosxsinx+xso Int(cos^2x)=1/2[cosxsinsx+x] and now add the constant!final answerIntegral of cos^2x=(1/2)(cosx sinx + x)+C = x/2 + (1/4)sin 2x + C(because sin x cos x = (1/2)sin 2x)Another method is:Use the half-angle identity, (cos x)^2 = (1/2)(1 + cos 2x). So we have:Int[(cos x)^2 dx] = Int[(1/2)(1 + cos 2x)] dx = (1/2)[[Int(1 dx)] + [Int(cos 2x dx)]]= (1/2)[x + (1/2)sin 2x] + C= x/2 +(1/4)sin 2x + C
