MATH 114 - Graphing, Antiderivatives, and Integrals

f’(c) =

f(b) - f(a) / b - a

Mean Value Theorem

lim x → ±∞ 1 / x^r

0

if r > 0

Antiderivative of f(x) + g(x)

F(x) + G(x) + C

where F’(x) = f(x) and G’(x) = g(x)

Antiderivative of kf(x)

where k is a constant

k F(x) + C

where F’(x) = f(x)

Antiderivative of f(x) - g(x)

F(x) - G(x) + C

where F’(x) = f(x) and G’(x) = g(x)

Antiderivative of xⁿ

n ≠ -1

xⁿ⁺¹ / n + 1

Antiderivative of sin(x)

-cos(x) + C

Antiderivative of cos(x)

sin(x) + C

Antiderivative of sec²(x)

tan(x) + C

Antiderivative of csc²(x)

-cot(x) + C

Antiderivative of sec(x)tan(x)

sec(x) + C

Antiderivative of csc(x)cot(x)

-csc(x) + C

Σⁿ_i=1 Q_i

Q₁ + Q₂ + Q₃ … + Q_n

Sigma Notation

Σⁿ_i=1 i

n(n+1) / 2

Σⁿ_i=1 i²

n(n+1)(2n+1) / 6

Σⁿ_i=1 i³

n²(n+1)² / 4

Σⁿ_i=1 c

nc

Σⁿ_i=1 (a_i ± b_i)

Σⁿ_i=1 a_i ± Σⁿ_i=1 b_i

Σⁿ_i=1 c a_i

c Σⁿ_i=1 a_i