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## 1.3 Integral Calculus

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**1.3 Integral Calculus**1.3.1 Line, Surface, Volume Integrals**For a given boundary line there many**different surfaces, on which the surface integral depends. It is independent only if If the surface is closed: b) surface integral:**2**2 2 Example 1.7**1.3.3 Fundamental Theorem for Gradients**The line integral does not depend on the path P.**Example 1.9**along I-II and III**1.3.4 Fundamental Theorem for Divergences**(also Gauss’s or Green’s theorem) The surface S encloses the volume V.**dz**dy dx**Example 1.10**Check the divergence theorem for**1.3.5 Fundamental Theorem for Curls**(also Stokes’ theorem) The path P is the boundary of the surface S. The integral does not depend on S.**dz**dy**Example 1.11**Check Stokes’ Theorem for