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Calculus Level 5

Find the length of the path traced by the function $f(x)=\dfrac x2 +\sin (4x)$ in the interval $[0,\pi]$ . Write your answer to 3 decimal places.

1 solution

Vishwak Srinivasan
May 12, 2015

The length of path of a function $y = f(x), x \in [a,b]$ is given by

$\large L = \color{#3D99F6}{\displaystyle \int_{a}^{b} \sqrt{1+ (\dfrac{dy}{dx})^2} dx}$

$y' = f'(x) = \frac{1}{2} + 4\cos 4x$

Rest is trivial and the integral is left as an exercise to reader.