Area and volume of cross sections between curves

Coefficient of semi-circle

Pi/8

Coefficient of square

1

Isosceles right triangle (side x is a leg) coefficient

1/2

Isosceles right triangle (side x is hypotenuse) coefficient

1/4

Equilateral triangle coefficient

(Sqrt(3))/4

Rectangle

K∫(f-g)²dx or ∫h(x)(f-g)dx

Washer/disk

Pi∫(f(x))² - (g(x))² dx

Shell

2pi∫r(x)(f(x)-g(x))dx

Arc length

∫Sqrt(1+f’(x))dx

Surface Area

2pi∫r(x)Sqrt(1+f’(x))dx