Volume of solid with base _______
∫ [multiplier] (top-bottom)^[something]
Frozen!
Frozen!
Boost!
Boost!
Integral area function formula square
Base²
Take deriv, plug in value
Revolve 2 equations over axis
π∫ top² - bottom²
Integral area function formula "base"
Top-bottom
Frozen!
Frozen!
Integral area function formula rectangle
Differentiable graph
No corner, cusp, vertical line
π∫ (axis - top)² - (axis - bottom)²
Integral area function formula semicircle
π/8 * base²
Integral area function formula equilateral triangle
(√3 )/4 * base²
"Left" and "right" functions are equal at point
No holes, jumps, asymptotes
Integral area function formula isosceles triangle
1/2 base²
Take deriv, plug in value
Boost!
Boost!
Integral area function formula rectangle
Base * height
Frozen!
Frozen!
Differentiable graph
Integral area function formula isosceles triangle
Continuous graph
No holes, jumps, asymptotes
Base²
∫ [multiplier] (top-bottom)^[something]
Continuous function
Integral area function formula "base"
Top-bottom
Integral area function formula equilateral triangle
Revolve 2 equations over axis
π∫ top² - bottom²
Frozen!
Frozen!
Integral area function formula semicircle
π/8 * base²
Revolve 2 equations over arbitrary line
π∫ (axis - top)² - (axis - bottom)²
Duel!