(a) Verify Green's theorem for $\oint_C (3x^2 - 8y^2) \, dx + (4y - 6…

Question

(a) Verify Green's theorem for $\oint_C (3x^2 - 8y^2) \, dx + (4y - 6xy) \, dy$, where $C$ is the boundary of the region defined by $x = 0$, $y = 0$ and $x + y = 1$.

(b) Verify divergence theorem for $\vec{F} = x\hat{i} + y\hat{j} + z\hat{k}$ taken over the cube bounded by $x = 0$, $x = a$, $y = 0$, $y = a$, $z = 0$ and $z = a$.

Related pages

• Euler's Theorem on Homogeneous Functions — topic
• Engineering Mathematics-I syllabus

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