Is It Possible? Solving Calculus Questions with Ease

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In summary, the conversation discusses the possibility of using calculus to solve a problem involving a derivative notation that is not actually a fraction. While it is not mathematically correct, it is a common practice to treat differential elements as fractions in order to simplify calculations. However, the bounds on the integral may need to be adjusted accordingly.
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NODARman
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Hi, just wondering if that's possible in calculus.
(See the attachment)
 

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  • #2
NODARman said:
TL;DR Summary: .

Hi, just wondering if that's possible in calculus.
(See the attachment)
What you wrote was essentially correct. But...

In reality? No. The derivative notation ##\dfrac{d \theta }{dt}## is not actually a fraction so you cannot cancel the dt's.

However, in practice you can "cancel" the dt's. It's a similar effect to the chain rule: ##\dfrac{d \theta }{dx} = \dfrac{d \theta }{dt} \cdot \dfrac{dt}{dx}##. Again, there is no real cancellation, but it appears that way.

Mathematicians in the 1800s spent a great deal of time showing how you can treat a differential element as a fraction. Most of the time you can get away with it.

-Dan
 
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  • #3
Technically the bounds on the integral need to change to ##\int_{t(0)}^{t(2\pi)}## if you are integrating wrt ##t##.
 
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Related to Is It Possible? Solving Calculus Questions with Ease

1. Is calculus difficult to learn?

Calculus can be challenging for some people, but with dedication and practice, it is possible to understand and solve calculus questions with ease.

2. What are the main concepts in calculus?

The main concepts in calculus are limits, derivatives, and integrals. These concepts are used to solve problems involving rates of change, optimization, and area/volume calculations.

3. How can I improve my calculus skills?

To improve your calculus skills, it is important to practice regularly and seek help from a tutor or teacher if needed. It can also be helpful to break down problems into smaller, more manageable steps.

4. What are some real-world applications of calculus?

Calculus has many real-world applications, such as in engineering, physics, economics, and statistics. It is used to model and solve problems involving motion, growth, and change.

5. Can calculus be used to solve problems in other fields of science?

Yes, calculus is a fundamental tool in many fields of science, including biology, chemistry, and computer science. It is used to analyze and model complex systems and relationships.

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