In this video, we compute the arc length of a parametric curve where x(t) =t^4/16 +1/(2t^2) and y(t) = t, from t = 1 to t = 3. We start by differentiating the x- and y-coordinates with respect to t, squaring the results, adding them, and simplifying the expression. Through careful factoring and simplification, we avoid unnecessary extra work. We then compute the integral of the square root of this expression from t = 1 to t = 3, arriving at an arc length of 49/9. I want to emphasize here the process of recognizing patterns in the simplification of such arc length computations.
#Mathematics #Calculus #ArcLength #ParametricCurves #Integration #Differentiation #MathTutorial #iitjammathematics #calculus2 #calculus3
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