Solving Integral of cosX^2: Tips and Advice

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In summary, the integral of cos(x^2) cannot be solved through ordinary methods but it is possible to solve (cosx)^2 by applying the half-angle formula. However, the proof for why it is not possible to solve cos(x^2) through ordinary methods would require an infinite series expansion of sin(x^2).
  • #1
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i want someone to help me with the integral of cosX^2



i attempted using integrals by parts.. wat i got when i differentiate it i didn't go back to the same integral equation.
is it that it is not possible??
 
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  • #2


evra said:
i want someone to help me with the integral of cosX^2

I'm not sure what you mean here. If you want to take the integral of [tex]\cos x^2[/tex], then this cannot be solved through ordinary methods. However, if you want to solve (cosx)^2, just apply the half-angle formula.
 
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  • #3
hi evra! :smile:
evra said:
i attempted using integrals by parts.. wat i got when i differentiate it i didn't go back to the same integral equation.
is it that it is not possible??

∫ cosx.cosx dx

= [sinx.cosx] + ∫sinx.sinx dx

= [sinx.cosx] + ∫ 1 dx - ∫cosx.cosx dx​

so 2∫ cosx.cosx dx = [sinx.cosx] + ∫ 1 dx :wink:

(or just use one of the standard trignonometric identites as gb7nash :smile: says)
 
  • #4


mr gb7nash, yes i mean ∫cos x^2. but the relation u used above can't work. i tried it but the rsult i got when i defferentiate it i can't come back to the original answer.
please check it.
 
  • #5
evra said:
i tried it but the rsult i got when i defferentiate it i can't come back to the original answer.
please check it.

nooo … you show us what you got :wink:
 
  • #6


i got sinX^2 and when I differentiate this I got 2XcosX^2
 
  • #7
evra said:
i got sinX^2 and when I differentiate this I got 2XcosX^2

(try using the X2 icon just above the Reply box :wink:)

no, if you want to find ∫ cos(x2) dx, then as gb7nash said, this cannot be solved through ordinary methods …

integration by parts, or the half-angle formula, will only work for ∫ cos2x dx :wink:
 
  • #8


then its not possible... thanks! its like sinX^2.
BUT why is it that its not possible.. what are the prooves? a younger brother is bordering me with it and he said i should give him concret mathematical proves.
thanks
 
  • #9


evra said:
then its not possible... thanks! its like sinX^2.
BUT why is it that its not possible.. what are the prooves? a younger brother is bordering me with it and he said i should give him concret mathematical proves.
thanks

It's possible with an infinite series expansion of sin(A), A=x^2
 
  • #10


no i don't think so because i did that and if i defferentiate the answer i got, i can't get back to sin(x2)
 

What is an integral?

An integral is a mathematical concept that represents the area under a curve. In other words, it is a way to find the total value or sum of a continuous function.

Why is it important to solve integrals?

Integrals are important in many fields of science, including physics, engineering, and economics. They are used to calculate important quantities such as displacement, velocity, and work. They also help to solve differential equations, which are fundamental in understanding many natural phenomena.

What are the steps to solve an integral?

The general steps to solve an integral are: identify the function to be integrated, apply appropriate integration rules or techniques, and evaluate the integral within the given limits. It is important to also simplify the integrand before integrating and to check for any necessary substitutions.

Are there specific tips for solving integrals of cosine squared?

Yes, there are several tips that can be helpful when solving integrals of cosine squared. One tip is to use the double angle formula, cos^2(x) = (1 + cos(2x))/2, to rewrite the integrand. Another tip is to use the half-angle formula, cos^2(x) = (1 + cos(x))/2, to simplify the integrand. It is also important to carefully determine the appropriate limits of integration when using these formulas.

Are there any common mistakes to avoid when solving integrals of cosine squared?

One common mistake to avoid is forgetting to add the constant of integration when evaluating the integral. Another mistake is incorrectly applying the double angle or half-angle formulas. It is also important to pay attention to the limits of integration and to properly substitute any variables before integrating.

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