Integration Area Under a Curve AP Calculus BC

Integration & Area Under a Curve AP Calculus BC March 20, 2017 Mrs. Agnew

Essential Stuff Essential Question • How do you evaluate definite integrals? Essential Vocabulary • General and Particular Antideratives • Definite Integral • Riemann Sum

Area Under a Curve • One of the major problems in calculus: how do you find the area bounded by a curve and an axis (or the area bounded by two curves) • One method for solving problem is Riemann Sums. • Riemann Sums gives an approximation for area bounded by curve and x-axis.

Riemann Sums Used to find area under a curve… Divide interval in equal subintervals Draw rectangles with endpoints on curve (either left or right) or midpoints on curve Find sum of the areas of the rectangles Another method is the Trapezoidal Rule Examples and calculator program

What Are Antiderivatives? • A function F is the antiderivative of f (x) if F’(x) = f(x) for all x over a given interval. • The general antiderivative of a function is F(x) + C, where C is an arbitrary constant. • If given a point on F, we can find the

Antidifferentiation Formulas Function Antiderivative Examples…

The Definite Integral Riemann Sums

Definite Integrals If a function f is continuous on the interval [a, b], then… where F is any antiderivative of f. Examples…

Suggested Homework • Section 4. 9 - #10, 11, 14, 20, 24, 25, 36, 41, 43 • Section 5. 2 - #1, 3, 7, 29, 30, 33, 36 • Section 5. 3 - #22, 24, 26, 30, 32, 33, 47 – 50