How do you find the arc length of the curve $y=e^(3x)$ over the interval [0,1]?

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Answer 1 · 2016-09-24T13:58:06

$19.14$

simple arc length formulation:

$s = int_C ds = int_(x_1)^(x_2) sqrt( 1+ (y')^2) dx$

here $y' = 3 e^(3x)$

$s = int_(0)^(1) sqrt( 1+ (3e^(3x))^2) dx$

the integration is not nice, here is computer solution:

$int sqrt(1+(3 e^(3 x))^2) dx = 1/3 (sqrt(9 e^(6 x)+1)-tanh^(-1)(sqrt(9 e^(6 x)+1)))+C$

The numerical solution is: $19.14$

How do you find the arc length of the curve y=e^(3x)y=e^(3x) over the interval [0,1]?