Computing the area of the region R = {(x, y) | x 1,0 y 1/x} gives...

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Computing the area of the region R = {(x, y) | x 1,0 y 1/x} gives rise to the integral 1 dx X and it is not difficult to show that this integral diverges, so the area of the region is infinite However, if the region R is rotated about the x-axis, the result is a finite volume. Find this volume. Volume = x+8 x+10x+9 so we a similar dx predict integrand converges the is integral e3x so we a similar predict converges da: integrand 4x+8 is the integral so we a similar L x3+1 dx predict x+10x+8 integrand diverges the is integral so we a similar 1 Soo x dx predict x+10x+8 integrand diverges the is integral Computing the area of the region R = {(x, y) | x 1,0 y 1/x} gives rise to the integral 1 dx X and it is not difficult to show that this integral diverges, so the area of the region is infinite However, if the region R is rotated about the x-axis, the result is a finite volume. Find this volume. Volume = x+8 x+10x+9 so we a similar dx predict integrand converges the is integral e3x so we a similar predict converges da: integrand 4x+8 is the integral so we a similar L x3+1 dx predict x+10x+8 integrand diverges the is integral so we a similar 1 Soo x dx predict x+10x+8 integrand diverges the is integral