CALC 2 EXAM 2 NOTES #10 2025-26
Area between curves
(x axis) - correct answer integral of upper function minus lower function a and b are
where the functions intersect (x values)
Area between curves
(y axis) - correct answer integral of upper function (right function) minus lower function
(left function) a and b are where the functions intersect (y values)
Volume by slicing - correct answer you must change the ith term to whatever the
variable is next to the δ (e.g. Xi needs to be with δx) (function of a disk shown)
Disks or washers - correct answer what shape(s) is/are yield during finding a volume by
slicing (function of a washer shown)
- correct answer could solve a problem purely algebraically to derive a function
Similar triangles - correct answer the method for finding a relation between two triangles
Pythagorean theorem - correct answer another method to find a relation between a
triangle (used to find similar triangles of circular objects)
Shell method - correct answer the method of integration in which you use cylindrical
shells to figure out the volume of a function
∫2πrhdx or ∫2πxif(xi)dx
Work - correct answer work = force * distance.
Force = mass * acceleration
Force - metric - correct answer f = mg. G = 9.8 m/s
Units -> newtons
Hook's law - correct answer f = kx (spring distance)
Density - correct answer mass / volume
English system mass = weight - correct answer density * volume
Arc length - correct answer √(1+ƒ'(x*)²)
Pressure - correct answer force / area (in general)
Hydrostatic pressure - correct answer (metric sys.) Density * g * depth. G = 9.8
(american sys.) Density * depth
Area between curves
(x axis) - correct answer integral of upper function minus lower function a and b are
where the functions intersect (x values)
Area between curves
(y axis) - correct answer integral of upper function (right function) minus lower function
(left function) a and b are where the functions intersect (y values)
Volume by slicing - correct answer you must change the ith term to whatever the
variable is next to the δ (e.g. Xi needs to be with δx) (function of a disk shown)
Disks or washers - correct answer what shape(s) is/are yield during finding a volume by
slicing (function of a washer shown)
- correct answer could solve a problem purely algebraically to derive a function
Similar triangles - correct answer the method for finding a relation between two triangles
Pythagorean theorem - correct answer another method to find a relation between a
triangle (used to find similar triangles of circular objects)
Shell method - correct answer the method of integration in which you use cylindrical
shells to figure out the volume of a function
∫2πrhdx or ∫2πxif(xi)dx
Work - correct answer work = force * distance.
Force = mass * acceleration
Force - metric - correct answer f = mg. G = 9.8 m/s
Units -> newtons
Hook's law - correct answer f = kx (spring distance)
Density - correct answer mass / volume
English system mass = weight - correct answer density * volume
Arc length - correct answer √(1+ƒ'(x*)²)
Pressure - correct answer force / area (in general)
Hydrostatic pressure - correct answer (metric sys.) Density * g * depth. G = 9.8
(american sys.) Density * depth
