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# (a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x-axis and (ii) the y-axis.(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.$x = \ln (2y + 1)$ , $0 \le y \le 1$

## a) $$=2 \pi \int_{0}^{1} \ln (2 y+1) \sqrt{1+\frac{4}{(2 y+1)^{2}}} d y$$b) $$x \text { -axis: } 4.2583, \quad y \text { -axis : } 5.6053$$

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Applications of Integration

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##### Kristen K.

University of Michigan - Ann Arbor

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