- #31
Justabeginner
- 309
- 1
cos(pi/2)= 0
cos(-pi/2)= 0
tan(pi/4)=1
tan(-pi/4)= -1 ?
cos(-pi/2)= 0
tan(pi/4)=1
tan(-pi/4)= -1 ?
Length of a Curve: Solve Homework Equation
Click For Summary
Homework Help Overview
The discussion revolves around finding the length of a curve defined by the integral equation \( y = \int_{-\pi/2}^x \sqrt{\cos t} \, dt \) for \( x \) in the range of \(-\pi/2\) to \(\pi/2\). Participants are exploring the application of the arc length formula and the differentiation of the integral to derive the necessary components for the calculation.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants discuss the differentiation of the integral and the implications of the fundamental theorem of calculus. There are questions about the correct interpretation of the limits of integration and the relationship between the variables involved. Some participants express confusion regarding the integration process and the application of the arc length formula.
Discussion Status
The discussion is active, with participants providing insights and corrections to each other's reasoning. Some have offered guidance on the differentiation process and the application of the fundamental theorem of calculus, while others are still grappling with the integration and the implications of the arc length formula.
Contextual Notes
There is a noted confusion regarding the limits of integration and the interpretation of the integral in terms of the variable \( x \). Participants are also questioning the assumptions about the relationship between the function and its derivative.
Similar threads
- · Replies 6 ·
- · Replies 5 ·
- · Replies 11 ·
- · Replies 3 ·
- · Replies 10 ·