The discussion revolves around evaluating integrals involving the dot and cross products of two vector functions, A(t) and B(t), defined in terms of the variable t. Participants are exploring the integration of these vector operations over a specified interval.
There are various attempts to compute the integrals, with some participants providing their results for the dot and cross products. However, there is no explicit consensus on the correct approach or final results, and some participants are still questioning their understanding of the problem.
Some participants have noted the need to show their work before receiving help, and moderators have emphasized the importance of posting in the appropriate forum for homework-related queries.
Integral of t = t2/2 = 2yusukered07 said:1. If A (t) = t i - t2j + (t -1) k, evaluate (b) [tex]\int^{2}_{0} A[/tex]
mathman said:Integral of t = t2/2 = 2
Integral of t2 = t3/3 = 8/3
Integral of (t-1)=t2/2 - t = 0
Net result 2i -(8/3)j
yusukered07 said:If A(t) = t i - t2 j + (t - 1) k and B(t) = 2t2 i + 6t k, evaluate (a) [tex]\int^{2}_{0}A \cdot Bdt ,[/tex] (b) [tex]\int^{2}_{0}A \times B dt.[/tex]
Redbelly98 said:Moderator's note: thread moved from "Calculus & Analysis"
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Start by evaluating A·B and AxB.