How do you graph an integral of f(x) = x?

  • Thread starter Thread starter courtrigrad
  • Start date Start date
  • Tags Tags
    Integration
AI Thread Summary
To graph the integral of f(x) = x, first calculate the integral, which is ∫x dx = (x²/2) + C, where C represents the constant of integration. This results in a family of parabolas, each corresponding to different values of C. The process involves finding the integral and then plotting the resulting function. Each graph will vary based on the chosen constant, illustrating the concept of a family of curves. Understanding this process is essential for accurately graphing integrals.
courtrigrad
Messages
1,236
Reaction score
2
How would you graph the integral of f(x) = x? What is the process to graph an integral?


Thanks
 
Physics news on Phys.org
Do you mean to graph this "beauty":
\int x \ dx =\frac{x^{2}}{2}+C

It's a family of parabolas...

Daniel.
 
oh ok. thanks a lot
 
The way to "graph an integral" is to first find the integral (which will involve a "constant of integration") and then integrate! Since you will have a different function for every value of C, you will, as dextercioby said, a "family" of graphs.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

Similar threads

Back
Top