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

Click For Summary
SUMMARY

This discussion focuses on solving multivariable calculus problems involving two variables, specifically integrals and derivatives. The problems presented include the integral \(\int \frac{1}{d-x} dx\), the derivative of \(f(t) = \sin(\omega t - 1)\), and the integral \(\int \frac{x}{(x^2 + L^2)^{3/2}} dx\). Key techniques for solving these problems include u-substitution, the chain rule, and trigonometric substitution. The participant emphasizes the importance of recognizing the correct substitution methods to avoid dead ends in problem-solving.

PREREQUISITES
  • Understanding of basic calculus concepts including integration and differentiation
  • Familiarity with u-substitution and trigonometric substitution techniques
  • Knowledge of the chain rule for derivatives
  • Experience with handling functions of multiple variables
NEXT STEPS
  • Study u-substitution in depth for integrals involving rational functions
  • Learn about the chain rule and its applications in multivariable calculus
  • Explore trigonometric substitution techniques for integrals
  • Practice solving problems involving derivatives and integrals of functions with two variables
USEFUL FOR

Students enrolled in multivariable calculus courses, educators teaching calculus concepts, and anyone looking to enhance their problem-solving skills in calculus involving multiple variables.

rmunoz
Messages
29
Reaction score
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. \int 1/(d-x) dx

2. derivative of f(t)= sin(\omegat -1)

3. \int 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
 
Physics news on Phys.org


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


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

Similar threads

Solve the given problem involving integration
  • · Replies 6 ·
Replies
6
Views
2K
Multivariable calculus problem involving partial derivatives along a surface
  • · Replies 9 ·
Replies
9
Views
2K
Integrals that keep me up at night
  • · Replies 22 ·
Replies
22
Views
3K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
Find f(x,y) given partial derivative and initial condition
  • · Replies 6 ·
Replies
6
Views
2K
Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
A question about the derivation of upper bound integrals
  • · Replies 23 ·
Replies
23
Views
2K
Applying integration to math problems
  • · Replies 5 ·
Replies
5
Views
2K
Determine limits of integration in double integral change of variables
  • · Replies 2 ·
Replies
2
Views
2K