Explanation Given: The Fundamental Theorem of Calculus I from single-variable, that is, if f is continuous on an open interval I and a be in I, then d d x ∫ a x f ( s ) d s = f ( x ) . Proof: Let r ( t ) = 〈 x ( t ) , y ( t ) , z ( t ) 〉 be continuous on an open interval I, and a be in I. So, x ( t ) , y ( t ) and z ( t ) must be continuous on open interval I, and the following results must be true. d d t ∫ a t x ( s ) d s = x ( t ) , d d t ∫ a t y ( s ) d s = y ( t ) , d d t ∫ a t z ( s ) d s = z ( t )

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

Videos

Question

Chapter 13.2, Problem 70E

To determine

To prove that second part of the Fundamental Theorem of Calculus for Vector-Valued Functions that if r(t) is continuous on an open interval I, and a be in I, then ddt∫atr(s)ds =r(t) by using the Fundamental Theorem of Calculus II from single-variable calculus.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 69E

Chapter 13.2, Problem 71E

Students have asked these similar questions

2. Suppose the population of Wakanda t years after 2000 is given by the equation f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000 people? Show all your work, round your answer to two decimal places, and include units. (4 points)

3. Solve the equation, give the answer exactly (no calculator approximations), and show all your work. (4 points) log5 2x = 3

Let I = f(x) dx, where f is the function whose graph is shown. 4 2 y f X 1 2 3 4 (a) Use the graph to find L2, R2 and M2. R₂ M2 = = = (b) Are these underestimates or overestimates of I? O 42 is an underestimate. O 42 is an overestimate. ◇ R2 is an underestimate. OR2 is an overestimate. OM2 is an underestimate. ○ M2 is an overestimate. (c) Use the graph to find T2. T₂ =

Chapter 13 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To prove that second part of the Fundamental Theorem of Calculus for Vector -Valued Functions that if r ( t ) is continuous on an open interval I, and a be in I, then d d t ∫ a t r ( s ) d s = r ( t ) by using the Fundamental Theorem of Calculus II from single-variable calculus.

Solution Summary: The author explains the Fundamental Theorem of Calculus for Vector-Valued Functions. If r(t) is continuous on an open interval I, and a be in I

Concept explainers

Videos

To prove that second part of the Fundamental Theorem of Calculus for Vector-Valued Functions that if r(t) is continuous on an open interval I, and a be in I, then ddt∫atr(s)ds =r(t) by using the Fundamental Theorem of Calculus II from single-variable calculus.

Want to see the full answer?

Chapter 13 Solutions