Question
Which theorem transforms surface integrals to volume integrals? State it.
Step 1
The theorem that transforms surface integrals into volume integrals is the Divergence Theorem, also known as Gauss's Theorem. Show more…
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Which of the following integrals expresses the volume obtained by rotating the area between $y=f(x)$ and $y=g(x)$ over $| a, b \}$ around the $x$ -axis? [Assume $f(x) \geq g(x) \geq 0 . ]$ $$ \begin{array}{l}{\text { (i) }(9+f(x))^{2}-(9+g(x))^{2}} \\ {\text { (ii) }(9+g(x))^{2}-(9+f(x))^{2}} \\ {\text { (iii) }(9-f(x))^{2}-(9-g(x))^{2}} \\ {\text { (iv) }(9-g(x))^{2}-(9-f(x))^{2}}\end{array} $$
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