Math Problem Statement
If C is the part of the circle (x4)2+(y4)2=1 in the first quadrant, find the following line integral with respect to arc length.
∫C(9x−8y)ds
Solution
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Math Problem Analysis
Mathematical Concepts
Line Integrals
Parametric Equations
Calculus
Arc Length
Trigonometry
Formulas
Equation of a circle: (x - h)^2 + (y - k)^2 = r^2
Parametric equations: x(θ) = h + cos(θ), y(θ) = k + sin(θ)
Arc length element: ds = sqrt((dx/dθ)^2 + (dy/dθ)^2) dθ
Line integral: ∫C f(x, y) ds
Theorems
Pythagorean Theorem
Fundamental Theorem of Line Integrals
Suitable Grade Level
Undergraduate Calculus (Grades 11-12 and above)