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Math Help - Fuel Consumption Question

  1. #1
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    Fuel Consumption Question

    The rate fuel is consumed by an aircraft is given by f(a,s)=10+a+\frac{s^2}{2} where a is its forward acceleration and s is its vertical acceleration. How much fuel did the aircraft consume over time interval [0,2] if (a,s) are given by the following parameterized curve:

    a(t)=\{{t },       t\in [0,1] and 2-t, t\in (1,2]

    AND

    s(t)=\{2, t\in[0,1] and 1, t\in(1,2]
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  4. #4
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    let \psi(t) = (a(t),s(t)) \text{ be a parameterization over } t \in S = [0,1]\cup(1,2]

    \psi(t) is a piecewise function:

    \psi(t) = \left\{\begin{array}{ll} (t,2) & \text{for } t\in [0,1] \\ (2-t,1) & \text{for } t\in (1,2] \end{array} \right.

    \therefore f\circ \psi(t) = \left\{\begin{array}{ll} 12+t & \text{for } t\in [0,1] \\ \frac{25}{2}-t & \text{for } t\in (1,2] \end{array} \right.

    Then calculate \int_S f\circ \psi(t) dt

    Edit: I'm not sure if this is right btw. You may have to take the sum of two double integrals over the two different domains.
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