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Justabeginner
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Homework Statement
Find the length of the curve given by the equation:
Homework Equations
[itex] y= \int_{-pi/2}^x √(cos t)\, dt [/itex] for x between -∏/2 and ∏/2
The Attempt at a Solution
y= sqrt (cos x)
dy/dx= (sin x)/[-2 * sqrt(cos x)]
So now applying the arc length formula of sqrt (1 + (dy/dx)^(2)), I get:
[itex] \int_{-pi/2}^{pi/2} sqrt(1 + {(sin^2(x))/(4 cos(x))}) \, dx [/itex]
[itex] \int_{-pi/2}^{pi/2} sqrt(1 + ({sin x * tan x}/4))\, dx[/itex]
I don't know how to integrate that, and haven't learned it either.. Any assistance is much appreciated. Thank you!
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