Let C be the curve $y = \frac{e^{1.9x} + e^{-1.9x}}{3.8}$, for $0.1 \le x \le 1.7$. A graph containing C follows. Find the surface area of revolution about the x-axis of C. First find and simplify $\sqrt{1 + y'^2} =$ Now find surface area =
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$$y = \frac{e^{1.9x} + e^{-1.9x}}{3.8}$$ $$y' = \frac{1}{3.8} (1.9e^{1.9x} - 1.9e^{-1.9x}) = \frac{1.9}{3.8} (e^{1.9x} - e^{-1.9x}) = \frac{1}{2} (e^{1.9x} - e^{-1.9x})$$ Show more…
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Let C be the curve y = (e^{2x} + e^{-2x})/4, for 0.1 <= x <= 1.6. A graph containing C follows. Find the surface area of revolution about the x-axis of C. First find and simplify sqrt(1+y'^2). Hint: The integrand for surface area is 2*pi*y*sqrt(1+(y')^2) dx. Now find surface area = 3.011137.
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