Calculus AP Formulas

Equals

• _a∫^c f(x)dx

• _a∫^b f(x)dx

• _b∫^c f(x)dx

• _c∫^a f(x)dx

Equals

• ∫ f(x)dx

• cx∫ f(x)dx

• c∫f(x)dx

• (1/c)∫f(x)dx

equals

• f(x)

• f(x) + C

• f '(x)

• f '(x) +C

• Intermediate Value Theorem
• Rolle's Theorem
• Average Rate of Change
• Average Value of f

• Average Rate of Change
• Average Value of f
• Intermediate Value Theorem
• Rolle's Theorem

Equals

• _d∫^cf(x)dx

• - _d∫^cf(x)dx

• f(d) - f(c)

• f(c) - f(d)

• f '(g'(x))
• f '(x)g'(x)
• f '(g(x))g'(x)
• f '(g(x)

• Volume using Washers
• Volume using Disks
• Volume using Shells
• Volume using Cross Sections

• f(x)
• f(x) + C
• f '(x)
• f '(x) + C

• c⋅f(x)
• c⋅f '(x)
• c⋅f '(x) + c⋅f(x)
• c⋅f '(x) - c⋅f(x)