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Mention the rules for differentiating and integrating
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Explanation of Solution
Description:
Rules for differentiating vector functions:
Consider,
u and v is the differentiable vector functions of t,
c is scalar,
C is a constant vector, and
f is differentiable scalar function.
1. Constant function rule:
2.
3.
4. Scalar multiple rule:
5. Chain rule:
6. Dot product rule:
7. Cross product rule:
For example:
Consider the position of a particle in the xy-plane
The position function is,
The expression for velocity of a particle is,
Substitute
At
The magnitude of the velocity
The expression for acceleration of a particle.
Substitute
At
The magnitude of the acceleration a is,
The expression to find the angle between two vectors a and b.
The expression to find the angle between two vectors a and b at time
Substitute
The above equation becomes,
Therefore, the angle between the velocity and acceleration vectors at given time is
Rules for integrating vector functions:
The indefinite integral of r with respect to t is the set of all antiderivatives of r. It is represented by
For example:
Integrate a vector function
Thus, the rules for differentiating and integrating vector functions is explained with an examples.
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Chapter 12 Solutions
University Calculus: Early Transcendentals (3rd Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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