Write the integral representing the area of the surface obta

Write the integral representing the area of the surface obtained by rotating the curve
y=e^x , 1 less than or equal to y less than or equal to 2, about the y-axis

please show work , thank you

Solution

when y=1, x=0

when y=2, x=ln(y)=ln(2)

20ln(2) x ds

=20ln(2) x sqrt(1+(y\')2) dx

=20ln(2) x sqrt(1+e2x) dx

Write the integral representing the area of the surface obtained by rotating the curve y=e^x , 1 less than or equal to y less than or equal to 2, about the y-ax

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