Consider the consider the region bounded by the graphs of x = y^2 and x =9. Find the volume of the solid that has this region as its base if every cross section by a plane perpendicular to the x axis has the shape of an equilateral triangle. Hint: if side of equilateral triangle is s, then area of the triangle is (√3)/4 * s^2
at (x,y) the base of the triangle is 2x.
That makes the area of the triangle √3 x^2
Adding up those slices of thickness dx, we have
v = ∫[0,9] √3 x^2 dx