Find a function from a given derivative

In summary, the conversation is about finding a function F that satisfies F(2) = 0 and F'(x) = sin(e^x). The person mentions that this may be related to the Fundamental Theorem of Calculus Part 2. They also reference the theorem and its equations. They attempt to integrate sin(e^x) but struggle. Finally, they come to the conclusion that the function F(x) = \int^{x}_{2} sin(e^t)dt satisfies the given criteria.
  • #1
notweNcaasI
1
0

Homework Statement


Find a function F such that F(2) = 0 and F'(x) = sin(e^x)

I think that this a reverse to Part 2 of the Fundamental Theorem of Calc but not really sure.

Homework Equations


From the Theorem:
A(x) = [tex]\int f(t) dt[/tex]

A'(x) = f(x)

f(t) = sin(e^x) ??


The Attempt at a Solution


I attempt to integrate sin(e^x) but that seems like a lost cause.

According to FTC II, the area function with lower limit a=2 is an antiderivative satisfying
F(2) = 0

F(x) = [tex]\int^{x}_{2} sin(e^t)dt[/tex]

Is this the correct function
 
Physics news on Phys.org
  • #2
That works fine.
 

1. What is the process of finding a function from a given derivative?

The process of finding a function from a given derivative involves using the rules of differentiation to work backwards. This means starting with the given derivative and finding the original function that would produce that derivative.

2. Why is it important to be able to find a function from a given derivative?

Being able to find a function from a given derivative is important because it allows us to solve problems and answer questions related to real-world situations. It also helps us understand the behavior and relationships between variables in mathematical models.

3. What are some common techniques used to find a function from a given derivative?

Some common techniques used to find a function from a given derivative include the power rule, the product rule, the quotient rule, and the chain rule. These rules help us find the original function by reversing the process of differentiation.

4. Are there situations where it is not possible to find a function from a given derivative?

Yes, there are some situations where it is not possible to find a function from a given derivative. This can happen when the derivative is not continuous or when the given derivative does not have a unique solution.

5. How can finding a function from a given derivative be useful in real life?

Finding a function from a given derivative can be useful in various fields such as physics, engineering, economics, and finance. It can help us model and predict the behavior of systems and make informed decisions based on the relationships between variables.

Similar threads

  • Calculus and Beyond Homework Help
Replies
6
Views
489
  • Calculus and Beyond Homework Help
Replies
3
Views
495
  • Calculus and Beyond Homework Help
Replies
23
Views
833
  • Calculus and Beyond Homework Help
Replies
15
Views
735
  • Calculus and Beyond Homework Help
Replies
3
Views
579
  • Calculus and Beyond Homework Help
Replies
2
Views
842
  • Calculus and Beyond Homework Help
Replies
18
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
454
  • Calculus and Beyond Homework Help
Replies
1
Views
646
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Back
Top