Integral area and volume equations duel

Continuous function

Integral area function formula square Base²

Integral area function formula "base" Top-bottom

Differentiable function

Integral area function formula rectangle Base * height

Revolve 2 equations over arbitrary line π∫ (axis - top)² - (axis - bottom)²

1/2 base²

Integral area function formula equilateral triangle (√3 )/4 * base²

Continuous graph

Revolve 2 equations over axis π∫ top² - bottom²

Volume of solid with base _______ ∫ [multiplier] (top-bottom)^[something]

Integral area function formula semicircle π/8 * base²

Differentiable graph No corner, cusp, vertical line

Base * height

Base²

Volume of solid with base _______ ∫ [multiplier] (top-bottom)^[something]

Integral area function formula "base"

Revolve 2 equations over axis π∫ top² - bottom²

Take deriv, plug in value

Differentiable graph

Continuous graph No holes, jumps, asymptotes

Revolve 2 equations over arbitrary line π∫ (axis - top)² - (axis - bottom)²

Integral area function formula isosceles triangle 1/2 base²

Continuous function "Left" and "right" functions are equal at point

π/8 * base²

Integral area function formula equilateral triangle (√3 )/4 * base²

End this game?