Compute the indefinite integral of the following function. r(t)=14ti+13+8tj+ln⁡19tk Select the correct choice below and fill in the answer boxes to complete your choice. A) ∫r(t)dt=()i+()j+()k B) ∫r(t)dt=()i+()j+()k+C

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Compute the indefinite integral of the following function.  r(t)=14ti+13+8tj+ln⁡19tk  Select the correct choice below and fill in the answer boxes to complete your choice.  A) ∫r(t)dt=()i+()j+()k  B) ∫r(t)dt=()i+()j+()k+C

May Dunn · Accepted Answer

Step 1  Solution:  Consider the vector-valued function:  r(t)=14ti+13+8tj+ln⁡19tk  Integrating with respect to t we have  ∫r(t)=[∫(14)tdt]i+[∫(13+8t)dt]+[∫(ln⁡19t)dt]k  sin⁡ce∫(14)tdt=14tln⁡14  ∫(13+8t)dt=18∫1udu(as put u=3+8t)  ∫(13+8t)dt=18ln|u|=18|3+8t| and   ∫(ln⁡19t)dt=(t(ln⁡19t)−t)  Putting these values in above we have  ∫r(t)=(14tln⁡14)i+(18ln|3+8t|)j+(t(ln⁡19t)−t)k+C

Compute the indefinite integral of the following function. r(t)

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