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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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