CALCULUS 2 FINAL FORMULAS 2025-26 #5
Volume Disk Method - correct answer π ∫ [R(x)]^2 dx - Horizontal Axis
Π ∫ [R(y)]^2 dy - Vertical Axis
Washer Method - correct answer π ∫ [R(x)^2 - r(x)^2] dx
R(x) - Outer Radius
R(x) - Inner Radius
Volume Shell Method - correct answer 2 π ∫ p(y) h(y) dy - Horizontal Axis
2 π ∫ p(x) h(x) dx - Vertical Axis
H - height
P - distance to axis of rotation
Arc Lenth - correct answer ∫ (1 + [f'(x)]^2)^(1/2) dx
Surface Area - correct answer 2 π ∫ r(x) (1 + [f'(x)]^2)^(1/2) dx
2 π ∫ r(y) (1 + [g'(y)]^2)^(1/2) dy
R - distance between graph and axis of revolution
Work - correct answer ∫ F(x) dx
Fluid Force - correct answer w ∫ h(y) L(y) dy
H - depth at fluid
L - Horizontal length of region
W = weight density
Pressure = w * h
Trig Integrals - Sin is odd - correct answer Convert to cosins, save one sin for du
Trig Integrals - Cos is odd - correct answer Convert to sins, save one cos for du
Trig Integrals - Sec is even - correct answer Convert to Tan, save sec^2 for du
Trig Integrals - Tan odd - correct answer Convert to sec, save sec tan for du
Trig Integrals - No secant factors - correct answer Convert one tan^2 to sec^2 - 1
Trig Sub - a^2 - u^2 - correct answer Let u = asinx
Volume Disk Method - correct answer π ∫ [R(x)]^2 dx - Horizontal Axis
Π ∫ [R(y)]^2 dy - Vertical Axis
Washer Method - correct answer π ∫ [R(x)^2 - r(x)^2] dx
R(x) - Outer Radius
R(x) - Inner Radius
Volume Shell Method - correct answer 2 π ∫ p(y) h(y) dy - Horizontal Axis
2 π ∫ p(x) h(x) dx - Vertical Axis
H - height
P - distance to axis of rotation
Arc Lenth - correct answer ∫ (1 + [f'(x)]^2)^(1/2) dx
Surface Area - correct answer 2 π ∫ r(x) (1 + [f'(x)]^2)^(1/2) dx
2 π ∫ r(y) (1 + [g'(y)]^2)^(1/2) dy
R - distance between graph and axis of revolution
Work - correct answer ∫ F(x) dx
Fluid Force - correct answer w ∫ h(y) L(y) dy
H - depth at fluid
L - Horizontal length of region
W = weight density
Pressure = w * h
Trig Integrals - Sin is odd - correct answer Convert to cosins, save one sin for du
Trig Integrals - Cos is odd - correct answer Convert to sins, save one cos for du
Trig Integrals - Sec is even - correct answer Convert to Tan, save sec^2 for du
Trig Integrals - Tan odd - correct answer Convert to sec, save sec tan for du
Trig Integrals - No secant factors - correct answer Convert one tan^2 to sec^2 - 1
Trig Sub - a^2 - u^2 - correct answer Let u = asinx
