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Theorem: Evaluating Line Integrals
The next theorem is useful for evaluating line integrals. It shows that any other parameter t can be used in place of the length s of the curve. Figure 13.2.6 illustrates the four parts of this theorem. THEOREM Let ∫C F · dS be a line integral.
Remark The integrals are sometimes called partial integrals. PROOF (i) and (ii) are special cases of (iii). (iii) is proved by a change of variables, (iv) is true because reversing the limits changes the sign of an ordinary integral.
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Home Vector Calculus Line Integrals Theorem: Evaluating Line Integrals |