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Ghella [55]
3 years ago
14

Evaluate the line integral using the fundamental theorem of line integrals. use a computer algebra system to verify your results

. cos(x) sin(y) dx + sin(x) cos(y) dy c
c.line segment from (0, −π) to 3π 2 , π 2 11
Mathematics
1 answer:
mario62 [17]3 years ago
7 0
\dfrac{\partial f}{\partial x}=\cos x\sin y\implies f(x,y)=\sin x\sin y+g(y)

\dfrac{\partial f}{\partial y}=\sin x\cos y=\sin x\cos y+\dfrac{\mathrm dg}{\mathrm dy}
\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C

f(x,y)=\sin x\sin y+C

\displaystyle\int_{\mathcal C}\cos x\sin y\,\mathrm dx+\sin x\cos y\,\mathrm dy=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(\frac{3\pi}2,\frac\pi2\right)-f(0,-\pi)=-1
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