How do you find the volume of the solid formed when the area in the first quadrant bounded by the curves #y=e^x# and x = 3?

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Answer 1 · 2018-07-27T17:40:27

#632.1337\ \text{unit}^3#

Volume of the solid generated by rotating about the x-axis, the region bounded by the curves #y=e^x# & #x=2# in the first quadrant, is given as

#\int \pi y^2\ dx#

#=\int_0^3\pi (e^x)^2\ dx#

#=\pi\int_0^3e^{2x}\ dx#

#=\pi[e^{2x}/2]_0^3#

#=\pi[e^{6}/2-e^0/2]#

#=\pi/2(e^6-1)#

#=632.1337\ \text{unit}^3#