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Question 2 Evaluate $\int (\sec^2 t \vec{i} + \frac{1}{t} \vec{j} + e^t \vec{k}) dt$ that satisfies the initial condition $\vec{r}(\pi) = \vec{i} + \vec{j} + \vec{k}$ and $t > 0$. [Select] A. $\vec{r}(t) = [1 + \tan t] \vec{i} + [\ln t + 1 - \ln \pi] \vec{j} + [e^t + 1 - e^\pi] \vec{k}$ B. $\vec{r}(t) = [1 + \tan t] \vec{i} + [\ln t - 1 - \ln \pi] \vec{j} + [e^t - 1 - e^\pi] \vec{k}$ C. $\vec{r}(t) = [\tan t] \vec{i} + [\ln t + 1 - \ln \pi] \vec{j} + [e^t + 1 - e^\pi] \vec{k}$ D. $\vec{r}(t) = [\tan t] \vec{i} + [\ln t - 1 - \ln \pi] \vec{j} + [e^t - 1 - e^\pi] \vec{k}$ E. $\vec{r}(t) = [1 + \tan t] \vec{i} + [\ln t + 1 - \ln t] \vec{j} + [e^\pi + 1 - e^t] \vec{k}$

          Question 2
Evaluate $\int (\sec^2 t \vec{i} + \frac{1}{t} \vec{j} + e^t \vec{k}) dt$ that satisfies the initial condition $\vec{r}(\pi) = \vec{i} + \vec{j} + \vec{k}$ and $t > 0$. [Select]
A. $\vec{r}(t) = [1 + \tan t] \vec{i} + [\ln t + 1 - \ln \pi] \vec{j} + [e^t + 1 - e^\pi] \vec{k}$
B. $\vec{r}(t) = [1 + \tan t] \vec{i} + [\ln t - 1 - \ln \pi] \vec{j} + [e^t - 1 - e^\pi] \vec{k}$
C. $\vec{r}(t) = [\tan t] \vec{i} + [\ln t + 1 - \ln \pi] \vec{j} + [e^t + 1 - e^\pi] \vec{k}$
D. $\vec{r}(t) = [\tan t] \vec{i} + [\ln t - 1 - \ln \pi] \vec{j} + [e^t - 1 - e^\pi] \vec{k}$
E. $\vec{r}(t) = [1 + \tan t] \vec{i} + [\ln t + 1 - \ln t] \vec{j} + [e^\pi + 1 - e^t] \vec{k}$

Question 2
Evaluate ∫ (sec^2 t i⃗ + (1)/(t)j⃗ + e^t k⃗) dt that satisfies the initial condition r⃗(π) = i⃗ + j⃗ + k⃗ and t > 0. [Select]
A. r⃗(t) = [1 + tan t] i⃗ + [ln t + 1 - lnπ] j⃗ + [e^t + 1 - e^π] k⃗
B. r⃗(t) = [1 + tan t] i⃗ + [ln t - 1 - lnπ] j⃗ + [e^t - 1 - e^π] k⃗
C. r⃗(t) = [tan t] i⃗ + [ln t + 1 - lnπ] j⃗ + [e^t + 1 - e^π] k⃗
D. r⃗(t) = [tan t] i⃗ + [ln t - 1 - lnπ] j⃗ + [e^t - 1 - e^π] k⃗
E. r⃗(t) = [1 + tan t] i⃗ + [ln t + 1 - ln t] j⃗ + [e^π + 1 - e^t] k⃗

Added by Alexander E.

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