Calc 2 Equations

sin^2(x) □ cos^2(x) = □ : + , 1

tan^2(x) □ 1 = □ : + , sec^2(x)

sin(x + y) = : sin(x)cos(y) + sin(y)cos(x)

cos(x - y) = : cos(x)cos(y) + sin(x)sin(y)

sin^2(x) = : (1/2) (1 - cos(2x))

sin(x)cos(y) = : (1/2) (sin(x + y) + sin(x-y))

∫f(x)g'(x) = : f(x)g(x) - ∫f'(x)g(x)dx

∫udv = : uv - ∫vdu

f(x) = x^nf'(x)= : nx^(n-1)

f(x) = x^n∫f(x)dx = : (x^(n+1))/(n+1) +C

f(x) = sin(x)f'(x) = : cos(x)

f(x) = sin(x)∫f(x)dx = : -cos(x) +C

f(x) = csc(x)f'(x) = : -csc(x)cot(x)

f(x) = csc(x)∫f(x)dx = : -ln(|csc(x)+cot(x)|) +C

f(x) = sinh(x)f'(x) = : cosh(x)

f(x) = sinh(x)∫f(x)dx = : cosh(x) +C

If you see a^2 - b^2 * x^2 : Usex = (a/b)sin(x)

If you see a^2 + b^2 * x^2 : Usex = (a/b)tan(x)

∫sec^n * tan(x)^m dxIf neither n is even or m is odd, : Use "ingenuity" ;)

Left Endpoint Approx. = : ΔX[f(X0)+...+f(Xn-1)]

For Approximations, ΔX = : (b-a)/n

Type 1 Improper Integral : ∫ {from a to ∞, -∞ to b, or -∞ to ∞}

Area "Under" a Curve (Polar) : A = (1/2) ∫(r^2)dθ { ∫(f(θ)^2)dθ }

Area "Between" two curves (Polar) : A = (1/2) ∫{(rin^2) - (rout^2)}dθ

Surface Area (Parametric) : SA = 2π ∫(r*L)dx{or dy, depending on how your slicing}

Hydro-static Force. F = : pg ∫L(y)D(y)dy

P Series:(Conditions: ) : If p > 1, then Σ{1/(n^p)} Converges.If p ≤ 1, then Σ{1/(n^p)} Diverges.Conditions: Must be of the form Σ{1/(n^p)}

Comparison Tests:(Conditions: ) : Σan ≥ ΣbnIf an Converges, bn Converges.If bn Diverges, an Diverges.Conditions: Non-Negative

Maclaurin Series for e^x = : Σ[0→∞] (x^n)/(n!)I = (-∞,∞)

Maclaurin Series for sin(x) = : Σ[0→∞] [((-1)^n)*x^(2n+1)]/((2n+1)!)I = (-∞,∞)

Maclaurin Series for (1 + X)^k = : Σ[n=0→∞] ("k choose n") * x^nI = (-1,1)

("k choose n") = : [k(k-1)(k-2)(k-3)...(k-n+1)]/(n!)