unit 7 Flashcards
1
Q
area between two curves equation
A
integral (f(top)-f(bottom))dx
2
Q
when to use disk method
A
Used when the solid is formed by rotating a region around a line, and the cross-section perpendicular to the axis of rotation is a circle.
3
Q
disk method equation
A
π ∫ f(x)^2 dx
4
Q
when to use washer method
A
Used when the solid has a hollow center, and the cross-section is a ring (a disk with a hole).
5
Q
washer method equation
A
V= π ∫ (R(outer x)^2 - R(inner x)^2) dx
6
Q
when to use shell method
A
Used when the cross-section is a cylindrical shell instead of a disk or washer.
7
Q
shell method equation
A
V= 2π ∫ (r(x) (h(x)) dx
8
Q
arc length equations
A
∫ root 1+ (f’(x))^2 dx
9
Q
surface area equations
A
2π ∫ (x-axis) root 1+f’(x) dx
