Respuesta :
the length of the arc of the curve from point P to point Q is
= 1/27 [85√(85) - 13√(13)]
What is the length of the arc of the curve?
Integral calculus addresses the geometrical idea of curve length.
Calculus offered a method for measuring the length of a curve by segmenting it into ever-tinier line segments or circle arcs. Combining such a procedure with the concept of a limit allows one to determine the precise length of a curve. A formula employing the integral of the function characterizing the curve serves as a summary of the entire process.
To find the length of the curve first we differentiate the equation with respect to any variable.
Than we square the both side of differentiate equation.
Than we integral of the equation
After that we put the limit of that variable against which we differentiate the equation and solve it to find the answer.
in this, we differentiate the x² = (y-4)³ with respect to y and solve it.
we get the length of the arc of the curve is 1/27 [85√(85) - 13√(13)]
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