Chapter 11: Q. 6 (page 900)

$Give precise mathematical definitions or descriptions of each of the concepts that follow . Then illustrate the definition with a graph or an algebraic example . the antiderivative of a vector function r (t)$

Short Answer

Expert verified

$\int r (t) dt = \int (x (t) i + y (t) j + z (t) k) dt = i \int x (t) dt + j \int y (t) dt + k \int z (t) dt$

Step by step solution

Step 1. Given information is:

A vector function r(t)

Step 2. Antiderivative of r(t)

$Let x = x (t), y = y (t), and z = z (t) be three real - valued functions with antiderivatives . \int x (t) dt, \int y (t) dt, and \int z (t) dt, respectively, on some interval I \subseteq R . Then the vector function \int r (t) dt = \int (x (t) i + y (t) j + z (t) k) dt = i \int x (t) dt + j \int y (t) dt + k \int z (t) dt is an antiderivative of the vector function r (t) = <x (t), y (t), z (t)> .$

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$Give precise mathematical definitions or descriptions of each of the concepts that follow . Then illustrate the definition with a graph or an algebraic example . the antiderivative of a vector function r (t)$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Antiderivative of r(t)

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Giveprecisemathematicaldefinitionsordescriptionsofeachoftheconceptsthatfollow.Thenillustratethedefinitionwithagraphoranalgebraicexample.theantiderivativeofavectorfunctionr(t)

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Antiderivative of r(t)

One App. One Place for Learning.

Most popular questions from this chapter

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$Give precise mathematical definitions or descriptions of each of the concepts that follow . Then illustrate the definition with a graph or an algebraic example . the antiderivative of a vector function r (t)$