Area Between a Graph and a Line: How Do We Find It?

  • Thread starter Thread starter intenzxboi
  • Start date Start date
  • Tags Tags
    Area Graph
Click For Summary
SUMMARY

The discussion focuses on finding the area between the graph of the function f(x) = 1 / (1 + x^2) and the line y = 1/2 using definite integrals. Participants emphasize the necessity of calculating the antiderivative of the function and applying limits of integration to determine the area accurately. Graphing the region is also recommended as a preliminary step to visualize the area in question.

PREREQUISITES
  • Understanding of definite integrals
  • Knowledge of antiderivatives
  • Familiarity with the function f(x) = 1 / (1 + x^2)
  • Basic graphing skills
NEXT STEPS
  • Study the process of calculating definite integrals
  • Learn how to find antiderivatives for various functions
  • Explore the graphical representation of functions and areas under curves
  • Investigate applications of integrals in real-world scenarios
USEFUL FOR

Students studying calculus, educators teaching integral calculus, and anyone interested in understanding the application of definite integrals in finding areas between curves.

intenzxboi
Messages
98
Reaction score
0

Homework Statement


Find area between
f(x) = 1 / 1+x^2 and the line y= 1/2


The Attempt at a Solution



would i need to take the anti derivative of it then minus 1/2??
 
Physics news on Phys.org
You'll need to use a definite integral, and the antiderivative is involved in the definite integral. You'll need limits of integration, too.

Have you graphed the region whose area you're trying to find? That would be a good start.
 

Similar threads

The integral of a function ##f(x)## from its graph
  • · Replies 15 ·
Replies
15
Views
2K
Stokes' Theorem for a Circle in a Plane
  • · Replies 7 ·
Replies
7
Views
3K
Finding Area using parametric equation
  • · Replies 12 ·
Replies
12
Views
2K
Derivative Problem: f’(1), f’(2), f’(3), and f’(5)
  • · Replies 11 ·
Replies
11
Views
2K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K
Area enclosed between this graph and the x-axis
  • · Replies 18 ·
Replies
18
Views
2K
Area enclosed between two graphs
  • · Replies 5 ·
Replies
5
Views
2K
Area between 2 polar equations
  • · Replies 1 ·
Replies
1
Views
2K
Finding the area of a double integral using dxdy instead of dydx
  • · Replies 4 ·
Replies
4
Views
3K
Find the area delimited by two polar curves
  • · Replies 2 ·
Replies
2
Views
2K