What is the Line Integral of a Semicircle with a 45 Degree Angle?

Click For Summary
SUMMARY

The discussion focuses on calculating the line integral of a semicircle defined by the angles \(\frac{5\pi}{4}\) to \(\frac{\pi}{4}\) with a radius \(a\). The integral is expressed as \(\frac{1}{a} \int dl\), where the x-component is identified as \(2a\). The primary question raised is regarding the determination of the y-component and the specific function to integrate over the semicircle. The discussion emphasizes the need for clarity on the integration function to complete the line integral calculation.

PREREQUISITES
  • Understanding of line integrals in calculus
  • Familiarity with polar coordinates and their applications
  • Knowledge of semicircular geometry and trigonometric functions
  • Basic proficiency in integral calculus
NEXT STEPS
  • Research the application of line integrals in vector fields
  • Study the conversion of Cartesian coordinates to polar coordinates
  • Learn about integrating functions over curves in calculus
  • Explore the properties of semicircles and their parametric equations
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus and vector analysis, as well as educators looking for examples of line integrals in practical applications.

mefisto666
Messages
12
Reaction score
0
so I have a semi circle that goes from

\frac{5\pi}{4} to \frac{\pi}{4}

so the angle between the x-axis the radius of the circle is 45 degrees.

I have, letting the radius = a)

\frac{1}{a} \int \.dl

this is going to have an x and y component, I know the x component is 2a in the direction of x, but what about the y component?
 
Last edited:
Physics news on Phys.org
What function are you integrating over that semi-circle?
 

Similar threads

High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Problem with calculating projections of curl using rotation of contour
  • · Replies 9 ·
Replies
9
Views
2K
High School Having trouble deriving the volume of an elliptical ring toroid
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Estimate the magnitude of a line integral exp(iz) over a semicircle
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Why is the integral of ##\arcsin(\sin(x))## so divisive?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Is My Calculus of Variations Approach Correct?
  • · Replies 12 ·
Replies
12
Views
3K
High School Why is this definite integral a single number?
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad Result of this integral in large Lambda limit
  • · Replies 12 ·
Replies
12
Views
3K