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Find the equation of the curve that passes through the point (x, y) = (0, 0) and has an arc length on the interval x is between 0 and pi over 4 inclusive given by the integral the integral from 0 to pi over 4 of the square root of the quantity 1 plus the secant to the 4th power of x, dx .

Respuesta :

LammettHash

[tex]\displaystyle\int_0^{\pi/4}\sqrt{1+\sec^4x}\,\mathrm dx=\int_0^{\pi/4}\sqrt{1+(\sec^2x)^2}\,\mathrm dx[/tex]

Recall that [tex]\displaystyle(\tan x)'=\sec^2x[/tex]. Then right away you see the integral gives the arc length of the curve [tex]y=\tan x[/tex] over the given interval.

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