Calculus BC AP Exam Formulas

Calculus BC AP Exam Formulas

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Section 1

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f'(x)=lim(h→0)

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Cards (68)

Section 1

(50 cards)

f'(x)=lim(h→0)

Front

[f(x+h)-f(x)]/h

Back

a²-u²

Front

u=asinΘ

Back

volume by disks for rotation about the y-axis

Front

Back

Integration by Parts

Front

∫udv=uv-∫vdu

Back

Mean Value Theorem for Derivatives

Front

f'(c)=(f(b)-f(a))/(b-a)

Back

∫du/(√(1-u²))

Front

sin⁻¹u+C

Back

Geometric form to maclaurin series

Front

a/(1-r)=∑arⁿ

Back

∫du/(1+u²)

Front

tan⁻¹u+C

Back

Arc Length of a Polar Equation

Front

L=∫√(r^2+(dr/dθ)^2) dθ

Back

∫sin u du

Front

-cos u + C

Back

∫cot u du

Front

ln|sin u| + C

Back

Definition of a definite integral

Front

∫(a→b)f(x)dx=lim(n→∞) ∑(i=1 to n) f(xi)Δx, where Δx=(b-a)/n and xi=a+iΔx

Back

Arc Length

Front

Back

∫tan u du

Front

-ln|cos u| + C

Back

x definition Polar

Front

x= r cos(θ)

Back

y definition Polar

Front

y= r sin(θ)

Back

cos(x) as a maclaurin series

Front

Back

∫(a^u)du

Front

(a^u)/(ln a) + C

Back

∫sec^2 u du

Front

tan u + C

Back

Trapezoid Rule

Front

∫f(x)dx= (b-a)/ 2n [f(x₀) + 2f(x₂) + 2f(x₃)..... f(x)]

Back

u²-a²

Front

u=asecΘ

Back

Taylor Polynomial

Front

=f(0)+f'(0)x+(f"(0)x²)/2!+ (f"'(0)x³)/3!+...+ (fⁿ(0)xⁿ)/n!

Back

∫e^u du

Front

e^u + C

Back

∫du/(u√(u^2-1))

Front

sec⁻¹u+C

Back

volume by washer around the x-axis

Front

Back

e^x as a maclaurin series

Front

Back

f'(x)=lim(x→a)

Front

[f(x)-f(a)]/(x-a)

Back

∫csc^2 u du

Front

-cot(u)+C

Back

∫csc u du

Front

-ln lcsc u + cot ul + C

Back

Average value of a function on the interval [a,b]

Front

average value=f(c)=∫f(x)dx/(b-a) with a and b as integral bounds

Back

Derivative for Parametric Equations

Front

(dy/dx)= (dy/dt)/(dx/dt) dx/dt≠0

Back

a²+u²

Front

u=atanΘ

Back

Odd- symmetry with respect to origin

Front

f(-x)=-f(x)

Back

Arc Length of a Parametric Curve

Front

L= ∫√( (dx/dt)^2 + (dy/dt)^2) dt

Back

Even- symmetry with respect to y-axis

Front

f(-x)=f(x)

Back

∫u^n

Front

(u^(n+1))/(n+1) + C, where u≠-1

Back

shell formula for revolution about the vertical line

Front

Back

volume of a solid of integrable cross-sectional area

Front

Back

∫cos u du

Front

sin u + C

Back

volume by disks for rotation about the x-axis

Front

Back

Cartesian to Polar conversion, Angle

Front

θ=tan⁻¹(y/x)

Back

Lagrange Remainder Formula

Front

Back

∫csc(u)cot(u) du

Front

-csc u + C

Back

Second derivative for Parametric Equations

Front

(d^2y)/(dx^2)=((d/dt)(dy/dx))/(dx/dt)

Back

∫sec(u)tan(u) du

Front

sec u + C

Back

Euler's Method

Front

y1 = y0 + f (x0,y0) (dx)

Back

Area enclosed by a Polar equation

Front

A=∫ 1/2 r∧₂ dθ

Back

sin(x) as a maclaruin series

Front

Back

∫sec u du

Front

ln lsec u + tan ul + C

Back

∫du/u

Front

ln|u|+C

Back

Section 2

(18 cards)

1+cot²(θ)

Front

csc²(θ)

Back

Dx[a^x]

Front

a^x*lna

Back

Dx[sinx]

Front

cosx

Back

Dx[cscx]

Front

-cscxcotx

Back

Dx[e^x]

Front

e^x

Back

Dx[lnx]

Front

1/x

Back

sin²(θ)+cos²(θ)

Front

1

Back

Dx[cotx]

Front

-csc²x

Back

2sin(θ)cos(θ)

Front

sin(2θ)

Back

Dx[sec⁻¹x]

Front

1/(x√(x²-1))

Back

Dx[secx]

Front

secxtanx

Back

Dx[tanx]

Front

sec²x

Back

tan²(θ)+1

Front

sec²(θ)

Back

Dx[sin⁻¹x]

Front

1/(√(1-x²))

Back

Dx[tan⁻¹x]

Front

1/(1+x²)

Back

cos²(θ)

Front

[1+cos(2θ)]/2

Back

Dx[cosx]

Front

-sinx

Back

sin²(θ)

Front

[1-cos(2θ)]/2

Back