Help With Calculus Question: Finding Value of F(r(t))

In summary, the conversation is about a question in a calculus book that is similar to a provided online solution. The person is having trouble getting the same value and is not sure if they are on the right track. However, the issue is resolved.
  • #1
Kris1
29
0
Hi,

My question in my Stewart Calculus book is the same as
http://faculty.tru.ca/smcguinness/M317W11/M317W11quiz4sol.pdf

However when I work out the solution I seem to get a different value. My solution is

integral from 0 to 2pi 16 <2cos^2t,2sin^2t,cos(t)sin(t)>
64 integral from 0 to 2pi -cos^2t*sin(t)+sin^2t+cos(t)

I'm not sure however as to whether I am on the right track. Can someone show me what the value of F(r(t)) is and if my solution is on the right track?

Sorry about the formatting.
 
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  • #2
Nevermind problem solved
 

What is Calculus?

Calculus is a branch of mathematics that deals with the study of rates of change and accumulation. It involves two main branches: differential calculus, which focuses on the instantaneous rate of change of a function, and integral calculus, which deals with the accumulation of quantities.

What is F(r(t)) in Calculus?

F(r(t)) is a notation used in calculus to represent a composite function. It means that the function r(t) is being plugged into the function f(x), where x is replaced by r(t). This allows us to find the value of f(r(t)) for a given value of t.

How do I find the value of F(r(t))?

To find the value of F(r(t)), you will need to first evaluate r(t) for the given value of t. This will give you a value for x, which you can then plug into the function f(x) to find the final result. Remember to follow the order of operations and use any given information, such as the domain of the function, to ensure accuracy in your calculations.

What is the chain rule in Calculus?

The chain rule is a fundamental rule in calculus that allows us to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

How can I improve my skills in solving Calculus problems?

The best way to improve your skills in solving Calculus problems is through practice. It is important to understand the concepts and theories behind the problems, but it is equally important to apply them in various scenarios. You can also seek help from a tutor or join study groups to get a better understanding of the subject.

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