Final answer:
To find the length of the curve, use the formula for arc length, which involves finding the derivative of each component function and evaluating the integral.
Step-by-step explanation:
To find the length of the curve, we can use the formula for arc length. In this case, the curve is defined by the vector function r(t) = 2t i + et j + e-t k. The formula for arc length of a vector function r(t) = f(t) i + g(t) j + h(t) k, where f(t), g(t), and h(t) are the component functions, is given by ∫√(f'(t)² + g'(t)² + h'(t)²) dt, where the integral is taken over the interval on which t is defined.
Using this formula, we can find the length of the curve as follows:
- Find the derivative of each component function.
- Plug these derivatives into the formula for arc length and evaluate the integral over the interval 0 ≤ t ≤ 9.
- Simplify the integral and calculate the length.