Saturday, July 26, 2014

Find the Length of the curve y=(x^4/8)+ (1/(4x^2)) on [1,3] For the derivative I got (x^3/2)-(1/(2x^3)) The square of that is x^6/4 + 1/4x^6 - 1/2...

You need to find the length of the given curve, on the interval [1,3], using the formula , where


You need to differentiate the equation of the curve , with respect to x, such that:









Notice that if you raise to square the binomial yields Now, in the last result, you have obtained hence, you may recognize the formula of special binomial product


You may take now the square root, such that:


Arc length =


Arc length =


You may evaluate the definite integral, such that:





Hence, evaluating the length of the curve , on interval yields .

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