Chapter 11: Q. 19 (page 872)

$What is the relationship between the graph of a differentiable vector function r (t) and the graph of \int r' (t) dt, one of the antiderivatives of r' (t) ?$

Short Answer

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$The graph of r (t) and r' (t) differ by a constant vector .$

Step by step solution

Step 1. Given information is:

$A differentiable vector function r (t)$

Step 2. Integrability of y=f(x) on [a,b]

$Let f : [a, b] \to R . Let f has an antiderivatives f on I . Then we say that f has an integral f on I and for any real constant c, we say F + c an indefinite integral of f over [a, b] denoted by \int f (x) dx . Thus, \int f = \int f (x) dx = F (x) + c The same thing applies to vector function also . So, \int r' (t) dt = r (t) + c, where c is a constant vector . Thus, the graph of r (t) and r' (t) differ by a constant vector .$

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$What is the relationship between the graph of a differentiable vector function r (t) and the graph of \int r' (t) dt, one of the antiderivatives of r' (t) ?$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Integrability of y=f(x) on [a,b]

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Whatistherelationshipbetweenthegraphofadifferentiablevectorfunctionr(t)andthegraphof∫r'(t)dt,oneoftheantiderivativesofr'(t)?

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Integrability of y=f(x) on [a,b]

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Geometry

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

$What is the relationship between the graph of a differentiable vector function r (t) and the graph of \int r' (t) dt, one of the antiderivatives of r' (t) ?$