Use the integration capabilities of a graphing utility to approximate the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

Question

y=√3x

y=x²

Round to 4 decimal places.

I have gotten 5.882 and 1.8721 and 6.53. All marked wrong.

Answer 1

It depends on whether it is the √(3)(x) or it is √(3x) is the x under the root or not?

If the x is NOT under the root and is separate you can do

∫₀^√(3)(π(3x²-x⁴)dx=6.5297 (rounded to 4 decimal places, you rounded to two 6.53)

If the x is under the root

∫₀^1.44224957(π(3x-x⁴)dx=5.8813 (this is the first answer you got but you rounded to 3 decimal places)