SECTION 4-3-B Area under the Curve. Def: The area under a curve bounded by f(x) and the x-axis and the lines x = a and x = b is given by Where and n is.

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Presentation transcript:

SECTION 4-3-B Area under the Curve

Def: The area under a curve bounded by f(x) and the x-axis and the lines x = a and x = b is given by Where and n is the number of sub-intervals

Area under the curve: Inscribed rectangle Circumscribed rectangle The sum of the area of the inscribed rectangles is called a lower sum, and the sum of the area of the circumscribed rectangles is called an upper sum

Area under the curve

The Exact area under a curve is given by: Where the number a is the lower limit of integration and b is the upper limit of integration f(x) must be continuous on the interval [a, b ]

Area under the curve bounded by the x-axis and the lines x=a and x=b

Area under the x-axis bounded by the curve and the lines x=a and x=b + - Use absolute value because there is no such thing as negative area

1) Find area bounded by the x-axis and

2) Find the area

3) Find area bounded by the x-axis and

4) Approximate using Left and Right hand Riemann sums with 6 equal subdivisions then compare to the exact area.

Homework Page 278 # 3-8, (even), 31, 38, 40, 41, 42, 43, 45, 47, 53 and 54 # 3-8 evaluate. no calculator #14-22 even. find the integral that will yield the area then evaluate using the calculator. # even. Find the area both geometrically and analytically, no calculator # 31 calculator #38,40 no calculator # 41,42,43 evaluate using the given values # 45 and 47 numerical # 53 and 54 compare