The length of the curve y = sin(3x) from x = 0 to 𝑥=𝜋6 is given by
Question
The length of the curve y = sin(3x) from x = 0 to 𝑥=𝜋6 is given by
Solution
The length of a curve, also known as arc length, for a function y = f(x) from x = a to x = b is given by the integral:
L = ∫ from a to b sqrt[1 + (f'(x))^2] dx
In this case, the function is y = sin(3x). The derivative of this function, f'(x), is 3cos(3x).
So, we need to compute the integral:
L = ∫ from 0 to π/6 sqrt[1 + (3cos(3x))^2] dx
This integral is not straightforward to compute, and it may require numerical methods or special functions to find an exact solution.
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