Question

Find r(t) if r'(t) = t⁵ İ + e² j + 2te²ᵗ k and r(0)=i + j + k.

Answer 1

To find r(t), you need to integrate r'(t). The final expression for r(t) is (1/6)t^6i + 2e^2j + (1/2)te^2t + i + j + k.

Step-by-step explanation:

To find r(t), we need to integrate r'(t). By integrating each component of r'(t), we get r(t) = (1/6)t^6i + 2e^2j + (1/2)te^2t + C. To find the value of C, we use the initial condition r(0) = i + j + k. Substituting t = 0 into r(t), we obtain C = i + j + k. Therefore, the final expression for r(t) is r(t) = (1/6)t^6i + 2e^2j + (1/2)te^2t + i + j + k.