Tag Archives: fundamental theorem of line integrals

Math2111: Chapter 5: Recommended reading: The fundamental theorems

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

In this entry we show that all the fundamental theorems (fundamental theorem of calculus, fundamental theorem of line integrals, Green’s theorem, Stokes’ theorem and the divergence theorem) are based on the same principle. Further, we will see that those theorems are all the fundamental theorems in \mathbb{R}, \mathbb{R}^2 and \mathbb{R}^3. Continue reading

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Math2111: Chapter 3: Line integrals. Section 3: Fundamental theorem of line integrals

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

Fundamental theorem of line integrals

The fundamental theorem of calculus gives a relation between the integral of the derivative of a function and the value of the function at the boundary, that is,

\displaystyle \int_a^b g^\prime(x)\,\mathrm{d} t= g(b)-g(a). \qquad\qquad\qquad\qquad\qquad (1)

The aim is now to find an analogous formula for line integrals. Continue reading