The discussion focuses on evaluating the dot and cross products of two vector functions, A(t) = t i - t² j + (t - 1) k and B(t) = 2t² i + 6t k. The integral of the dot product over the interval from 0 to 2 results in the expression 2t³ + 6t² - 6t, which can be integrated to yield a specific numerical result. The cross product yields -6t³ i + (2t³ - 8t²) j + 2t⁴ k, which also requires integration over the same interval. The discussion emphasizes the necessity of showing initial attempts at solving the problem to receive assistance.
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Integral of t = t2/2 = 2yusukered07 said:1. If A (t) = t i - t2j + (t -1) k, evaluate (b) \int^{2}_{0} A
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) \int^{2}_{0}A \cdot Bdt , (b) \int^{2}_{0}A \times B dt.
Redbelly98 said:Moderator's note: thread moved from "Calculus & Analysis"
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