06. CTRV Integral 2

CTRV Integral Position

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The general form of the solved integral can be found here .

Question 1: vktktk+1cos(ψk+ψk˙(ttk)) dt v_k \int_{t_k}^{t_{k+1}} cos(\psi_k + \dot{\psi_k} \cdot (t - t_k)) \space dt = ???

A. ψkvk˙(cos(ψk)sin(ψk)) \Large \frac{\psi_k}{\dot{v_k}}(cos(\psi_k) - sin(\psi_k))

B. vkψk˙(sin(ψk+ψk˙Δt)sin(ψk)) \Large \frac{v_k}{\dot{\psi_k}}(sin(\psi_k + \dot{\psi_k}\Delta t) - sin(\psi_k))

1) Which of the above (☝) options solves the given integral?

SOLUTION: B

Question 2: vktktk+1sin(ψk+ψk˙(ttk)) dt v_k \int_{t_k}^{t_{k+1}} sin(\psi_k + \dot{\psi_k} \cdot (t - t_k)) \space dt = ???

A. vkψk˙(cos(ψk+ψk˙Δt)+cos(ψk)) \Large \frac{v_k}{\dot{\psi_k}}(-cos(\psi_k + \dot{\psi_k}\Delta t) + cos(\psi_k))

B. ψkΔt(tan(ψk)sin(ψk)) \Large \frac{\psi_k}{\Delta t}(tan(\psi_k) - sin(\psi_k))

2) Which of the above (☝) options solves the given integral?

SOLUTION: A