What You NEED To Know In Calculus The fundamental theorem of calculus is used to evaluate definite integrals using antiderivatives. It is central to the evaluation of integrals, allowing you to find the area under a curve or between two functions. If f is continuous at every point of [a, b], and if F is any antiderivative of f on [a, b] then: ∫ a b f(x)dx = F(b) – F(a) Example: Find ∫ 3 (x3 + 1)dx -1 ∫ 3 (x3 + 1)dx x4 = 4 -1 Antiderivative of (x3 + 1) +x ] 3 -1 Antiderivative evaluated at 3 = (81 / 4 + 3) – (1 / 4 – 1) = 24 Antiderivative evaluated at -1 This rule is used in calculus when you want to find the derivative of a function that is a quotient. Hi Lo LoDeHi-HiDeLo Lo2 Example: Find f’(x)=x2-1 2 x +1 Hi=x2-1 DeHi=2x 2 Lo=x +1 DeLo=2x 2 2 F’(x)= (x +1) (2x)-(x -1)(2x) 2 (x +1)2 The Chain Rule applies whenever there is a function that is formed from two simpler function. F(x)= g(h(x)) >>>> F(x)= g’(h(x)) h’(x) Example: (sin(2x))’=2sin(x)cos(x) (sin(2x))’=2(sin’(x)cos(x)+sin(x)cos’(x)) (sin(2x))’=2(cos2(X)-sin2(x)) (sin(2x))’= 2cos(2x) f’’’(x) To get the Jerk of an equation is to take the derivative of that equation 3 separate times. f’’’(x) Example: Find the Jerk of 4x5. 1st Der.: 20x4 2nd Der.: 80x3 3rd Der.: 240x2 Works Consulted Finney, Ross, Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus. New Jersey: Pretince Hall, 2003. Print. Kahn, David S. Cracking the AP Calculus AB & BC Exams. New York: Random House, 2009. Print.