unit 7

Question 1

area between two curves equation

Answer 1

integral (f(top)-f(bottom))dx

Question 2

when to use disk method

Answer 2

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.

Question 3

disk method equation

Answer 3

π ∫ f(x)^2 dx

Question 4

when to use washer method

Answer 4

Used when the solid has a hollow center, and the cross-section is a ring (a disk with a hole).

Question 5

washer method equation

Answer 5

V= π ∫ (R(outer x)^2 - R(inner x)^2) dx

Question 6

when to use shell method

Answer 6

Used when the cross-section is a cylindrical shell instead of a disk or washer.

Question 7

shell method equation

Answer 7

V= 2π ∫ (r(x) (h(x)) dx

Question 8

arc length equations

Answer 8

∫ root 1+ (f’(x))^2 dx

Question 9

surface area equations

Answer 9

2π ∫ (x-axis) root 1+f’(x) dx