How to calculate this? $\oint x d x$ $ointxdx$

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How to calculate this? $\oint x d x$ $ointxdx$

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Answer 1 · 2018-04-08T08:19:47

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Explanation:

$x d x = \frac{1}{2} d (x^{2})$ $xdx = 1/2 d(x^2)$

Thus, its integral over any curve is the value of $\frac{1}{2} x^{2}$ $1/2x^2$ at the end minus its value at the end. Since for a closed curve, the beginning and the end are the same points, the two values cancel

$\oint x d x = 0$ $oint xdx = 0$

This is true in general whenever the differential to be integrated over a closed loop is an exact differential.

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How to calculate this? $\oint x d x$ $ointxdx$

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How to calculate this?∮xdxointxdx

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How to calculate this? $\oint x d x$ $ointxdx$