What's Next in Calculus: Solving Volumes with Integrals

  • Thread starter physicsed
  • Start date
  • Tags
    Volumes
In summary, the conversation was about solving a problem involving volumes in calculus. The integral \int^{1}_{2} \pi \frac{1}{x} dx was discussed, with a reminder to check the setup in the textbook. The correct antiderivative was determined to be \pi \int^{2}_{1} \frac{1}{x^2} dx = \pi [-\frac{1}{x}] from a power law perspective. The conversation also touched on grammar and ended with a positive note.
  • #1
physicsed
52
0
[SOLVED] volumes... last week of calc

i was absent when we went over the volume section.

y= 1/x, x= 1, x= 2, y= 0,; about the x-axis

[tex]
\int^{1}_{2} \pi \frac{1}{x} dx
[/tex]

i don't know what's next. can anyone inform me, please
 
Physics news on Phys.org
  • #2
You could actually do the integration, but that would be wrong because you haven't set it up right either. You integrate pi*r^2 where r is the radius of the disk over the volume. I'd suggest checking a few examples in your textbook.
 
  • #3
[tex]\int^{1}_{2} \pi [\frac{1}{x}]^2 dx[/tex]

if you help me with this problem, i am sure i will get the rest of the problems.
 
  • #4
It's a power law integral. Like x^n. What's n in this case? What's the antiderivative?
 
  • #5
[tex] \pi \int^{2}_{1} \frac{1}{x^2} dx[/tex]
 
Last edited:
  • #6
Fine start. Now what's the antiderivative of 1/x^2?
 
  • #7
[tex] \pi [ \frac{x^{-3}}{-3}] [/tex]
 
  • #8
Beep. Wrong. The antiderivative of x^n is x^(n+1)/(n+1). What's n in this case? Unless that's a careless error because you are paying more attention to texing than thinking, you may have missed more than 'volumes'.
 
Last edited:
  • #9
since it's divided by 1, isn't it negative n
=x^-2
 
  • #10
Yes, it is. Can you fix your antiderivative?
 
  • #11
(-1/3)x^-3
 
  • #12
Beep. Beep. Beep. You goofed it again. What's -2+1? Think this time.
 
  • #13
righttt

pi [(1/-1)x^-1]
 
  • #14
physicsed said:
righttt

pi [(1/-1)x^-1]

Much better! You've got it now, right? And you promised that meant you could get all the others.
 
  • #15
thanks buddy

your awesome
 
  • #16
It's "you're awesome". I'm correcting grammar tonight. Thanks.
 

1. What is a volume in calculus?

In calculus, volume refers to the measure of three-dimensional space occupied by an object or a region. It is typically calculated using integrals and is an important concept in many applications of calculus, such as in physics and engineering.

2. How is volume calculated in calculus?

In calculus, volume is calculated using integrals, which is a mathematical concept used to find the area under a curve. To find the volume of a three-dimensional object, we can break it down into infinitesimally small slices and use integrals to sum up the volumes of these slices. This process is known as integration.

3. What is the difference between area and volume in calculus?

Area and volume are both measures of space, but they differ in the dimension they describe. Area is a two-dimensional measure, while volume is a three-dimensional measure. In calculus, area is typically calculated using integrals of a curve, while volume is calculated using integrals of a surface.

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

Volume is a crucial concept in many fields, such as physics, engineering, and architecture. It is used to calculate the volume of liquids, the displacement of objects, and the capacity of containers. It is also used in optimization problems, such as finding the maximum volume of a box that can be made from a given sheet of material.

5. How can I improve my understanding of volumes in calculus?

To improve your understanding of volumes in calculus, it is important to practice solving problems and familiarize yourself with the different techniques and formulas used to calculate volume. You can also seek help from a tutor or attend study groups to clarify any doubts or misconceptions you may have. Additionally, making connections between volume and real-world applications can also help solidify your understanding.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
639
  • Calculus and Beyond Homework Help
Replies
9
Views
921
  • Calculus and Beyond Homework Help
Replies
3
Views
268
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
917
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
837
  • Calculus and Beyond Homework Help
Replies
6
Views
505
  • Calculus and Beyond Homework Help
Replies
10
Views
282
  • Calculus and Beyond Homework Help
Replies
1
Views
869
Back
Top