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yusukered07
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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]
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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
You need to show an attempt at solving the problem before receiving help!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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You need to show an attempt at solving the problem before receiving help!
Start by evaluating A·B and AxB.
Vector integration is a mathematical technique used to integrate vector-valued functions. It involves calculating the area under a vector curve, similar to how traditional integration calculates the area under a scalar curve.
Vector integration is important in science because many physical quantities, such as velocity and force, are represented by vectors. By integrating these vector quantities, we can determine important properties such as displacement and work.
Vector integration differs from traditional integration in that it involves not only calculating the area under a curve, but also taking into account the direction and magnitude of the vector values. This adds an additional level of complexity to the integration process.
Vector integration has numerous applications in fields such as physics, engineering, and computer graphics. It can be used to analyze the motion of objects, calculate the work done by a force, and determine the flow of fluids in a system.
Yes, there are several techniques for solving vector integration problems, including the use of line integrals, surface integrals, and volume integrals. These techniques involve breaking down the integration into smaller, more manageable parts and using specific formulas to solve for the final result.