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डाइवर्जेन्स प्रमेय (Divergence Theorem) का उपयोग करके, हम पृष्ठ समाकल (surface integral) को आयतन समाकल (volume integral) में बदल सकते हैं। डाइवर्जेन्स प्रमेय के अनुसार: \[ \iint_{S} \vec{F} \cdot d\vec{S} = \iiint_{V} (\nabla \cdot \vec{F}) \, dV \] जहाँ \(\vec{F} = y^{2}z\hat{i} + y^{3}\hat{j} + xz\hat{k}\) और \(V\) घन \(-1 \leq x \leq 1\), \(-1 \leq y \leq 1\), \(0 \leq z \leq 2\) द्वारा परिभाषित है। ### चरण 1: \(\nabla \cdot \vec{F}\) की गणना करें \(\nabla \cdot \vec{F}\) की गणना करने के लिए, हम \(\vec{F}\) के प्रत्येक घटक का आंशिक ______ ________ ________ _______ _____ _______ _______ __________ __________ ______ _______ _____.
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