- #1
doey
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i facing a maths problem in integrating ∫ cos^2(∏/2cosθ) with limit from 0 to ∏/2,i was panic and struggled a long period of time in solving this,anyone can help me? pls give me the answer in detail tq !
doey said:i facing a maths problem in integrating ∫ cos^2(∏/2cosθ) with limit from 0 to ∏/2,i was panic and struggled a long period of time in solving this,anyone can help me? pls give me the answer in detail tq !
micromass said:First of all, do you mean
(1) [itex]\int_0^{\pi/2} \cos^2 (\frac{\pi}{2} \cos\theta) d\theta[/itex]
or
(2) [itex]\int_0^{\pi/2} \cos^2 (\frac{\pi}{2\cos \theta}) d\theta[/itex]
Also, which methods do you have at your disposal? Contour integration? Differentiation under the integral sign? Just normal calc II techniques?
doey said:(1) [itex]\int_0^{\pi/2} \cos^2 (\frac{\pi}{2} \cos\theta) d\theta[/itex]
,i am asking this pls let me know the steps it takes
arildno said:Just a thought:
We may easily rewrite this equation into the identity:
[tex]\int_{0}^{\frac{\pi}{2}}\cos^{2}(\frac{\pi}{2}\cos\theta)d\theta+\int_{0}^{\frac{\pi}{2}}\sin^{2}( \frac{\pi}{2}\cos\theta)d\theta=\frac{\pi}{2}[/tex]
I feel dreadfully tempted to declare the two integrals to have the same value (the latter being merely a flipped version of the first), but temptation is not proof..
Integration is a mathematical process that involves finding the area under a curve or the accumulation of a quantity over a given interval. It is the inverse operation of differentiation and is used to solve a variety of problems in physics, engineering, economics, and other fields.
cos^2(∏/2cosθ) is a trigonometric function that represents the squared cosine of the angle (∏/2cosθ). The angle (∏/2cosθ) is dependent on the value of θ, which is a variable in the equation. This function is commonly used in integration problems.
The process of integrating cos^2(∏/2cosθ) involves using integration techniques such as substitution, integration by parts, or trigonometric identities to rewrite the function in a simpler form. The integral is then evaluated using rules and formulas to find the solution.
Integration cos^2(∏/2cosθ) is important because it allows us to solve a wide range of problems involving areas, volumes, and rates of change. It is also used in various fields of science and engineering to model and analyze real-world phenomena.
Some applications of integration cos^2(∏/2cosθ) include finding the area under a curve, calculating the volume of a solid, determining the average value of a function, and solving differential equations. It is also used in physics to analyze motion and in economics to optimize production and consumption.