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The area of the region bounded between the line x=3x=3 and the parabola y2=6xy^2=6x is:

Solution

✅ Correct Option: 2

By symmetry about the x-axis, the area is 2∫036x dx2\int_0^3 \sqrt{6x}\,dx.

=26⋅23[x3/2]03=26⋅23⋅33=418=122= 2\sqrt{6}\cdot\dfrac{2}{3}\left[x^{3/2}\right]_0^3 = 2\sqrt{6}\cdot\dfrac{2}{3}\cdot 3\sqrt{3} = 4\sqrt{18} = 12\sqrt{2} square units.

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