Determine el volumen resultante de rotar la función \( f(x) = \frac{1}{x} \), desde \( x = 1 \) hasta \( x = 2 \), alrededor del eje y usando el método de lavadoras.

\( y=\sinh (x) \)

Discur the convergene at \( [1,2] \) given that \( f(x)=x^{3}-x-1 \)

Find the area of the region bounded by the curves \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) and the line \( y = 1 \).

Find the volume of the solid obtained by rotating the region enclosed by \( y = 3x - x^2 \) and the x-axis for \( 0 \leq x \leq 3 \) around the x-axis using washers.

\( \int _ { 27 } ^ { 1063 } \frac { 23.68 + 5.19 \times 10 ^ { - 3 } T } { T } d T - \frac { 12760 } { 1063 } + \int _ { 1063 } ^ { 1127 } \frac { 29.29 } { T } d T \)