The base of S is the region enclosed by the parabola y = 4 − 4x2 and the x-axis. Cross-sections perpendicular to the x-axis are isosceles triangles with height equal to the base.

Answer 1

Volume v = ∫_-1¹1/2(4 - 4x²)²dx = 16∫₀¹(1 - 2x² + x⁴)dx = 16(x - 2x³/3 + x⁵/5)₀¹ = 128/15