?In Exercises 1 - 4, verify Green's Theorem by evaluating both integrals \(\int_{C} y^{2} d x+x^{2} d y=\int_{R} \int\left(\frac{\partial N}{

Chapter 15, Problem 2

(choose chapter or problem)

In Exercises 1 -  4, verify Green's Theorem by evaluating both integrals

\(\int_{C} y^{2} d x+x^{2} d y=\int_{R} \int\left(\frac{\partial N}{\partial x}-\frac{\partial M}{\partial y}\right) d A\)

for the given path.

C: boundary of the region lying between the graphs of y = x and \(y=\sqrt{x}\)

Text Transcription:

int_C y^{2} dx + x^{2} dy = int_R int(partial N / partial x - partial M / partial y) dA

y = sqrt{x}