Solved: Find the area of the surface obtained by revolving the, Mathematics

Find the area of the surface obtained by revolving the

Find the area of the surface obtained by revolving the curve: y=√(2 + 3x), 0≤x≤2 about the x-axis.

The answer is (pi/18)((41)^3/2- (17)^3/2)...... but I got (pi/6)((25)^3/2 - (9)^3/2). Where did I go wrong? My professor seems to have a (1/3) outside of the radical and I am not sure where it came from. Your helpful explanation is much appreciated!

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Mathematics: Find the area of the surface obtained by revolving the

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