How to Solve Multivariable Calculus Problems with Two Variables: Tips and Tricks

In summary, the conversation was about a student struggling with three problems involving integrals and derivatives with multiple variables. The problems included an integral with a substitution, a derivative with the chain rule, and an integral with a trig substitution. The student had tried various methods but was still having difficulty solving the problems.
  • #1
rmunoz
30
0
Integral and Derivative Help!

Homework Statement


I have 3 problems that i am struggling to solve for the simple fact that there are two variables in each problem. I have no experience with multivariable calculus... i feel like I am missing something big because i have all the prerequisites for this physics course completed and with high grades yet this is our first hw... stuff we should be familiar with.
1. [tex]\int[/tex] 1/(d-x) dx

2. derivative of f(t)= sin([tex]\omega[/tex]t -1)

3. [tex]\int[/tex] x/((x^2)+(L^2))^(3/2) dx

Homework Equations





The Attempt at a Solution


I've tried to solve 1 and 3 using trig substitution, partial fractions, integration by parts, u substitution but they all seem to lead to dead ends
 
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  • #2


Assume 'd' and 'L' are constants. The first is a simple u-substitution. The second one, apply the chain rule.
 
  • #3


The third one is a simple substitution as well. You could also do it with a trig substitution.
 

FAQ: How to Solve Multivariable Calculus Problems with Two Variables: Tips and Tricks

What is the difference between an integral and a derivative?

An integral is a mathematical operation that calculates the area under a curve, while a derivative is a mathematical operation that calculates the slope of a curve at a specific point.

Why are integrals and derivatives important in science?

Integrals and derivatives are important because they allow us to model and understand various physical phenomena, such as motion, growth, and change. They are also fundamental in many branches of science, including physics, chemistry, and engineering.

What are some real-world applications of integrals and derivatives?

Integrals and derivatives have many real-world applications, such as calculating the velocity and acceleration of an object, finding the area and volume of irregular shapes, and modeling population growth and decay. They are also used in fields like economics, biology, and medicine.

How can I learn more about integrals and derivatives?

There are many resources available to learn about integrals and derivatives, including textbooks, online tutorials, and educational videos. You can also consult with a math tutor or take a class specifically focused on these concepts.

What are some common mistakes people make when working with integrals and derivatives?

Some common mistakes people make when working with integrals and derivatives include forgetting to apply the chain rule or the product rule, using the wrong limits of integration, and incorrectly setting up the integral or derivative in terms of the variable of interest. It's important to carefully check your work and practice regularly to avoid these mistakes.

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