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. I only get one more try on the homework. I just can't figure it out.

Answer 1

y = √3 x and y = x² intersect at x = 0 and x = √3 - Solve √3 x = x² or x² - √3 x = 0 or (x - √3)x = 0

Then, as we are revolving about the x-axis, we calculate ∫π f(x)² for the 2 equations from 0 to √3 and subtract

∫π (√3 x )2 - ∫π (x²)² = ∫π (3x² ) - ∫πx⁴ = π(x³ - x⁵/5) evaluated at 0 and √3 π ( (√3)³ - (√3)⁵/5 ) = (6/5)√3 π =

6.53