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(3x^{2}-x^{4})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-x^{4})dx=5.8813 (this is the first answer you got but you rounded to 3 decimal places)