Definite Integration Say good-bye to C

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Presentation transcript:

Definite Integration Say good-bye to C Section 4-2-a Definite Integration Say good-bye to C

1st Fundamental Theorem of Calculus If a function is continuous on the closed interval [a,b] and F is an antiderivative of f on the interval, then The constant C is not necessary because

Notation for Definite Integrals a and b are called the limits of integration. They are attached to the integral symbol. The lower limit a is usually a left side boundary and the upper limit b is usually a right side boundary. Integrating produces an answer called the definite integral value.

2) Evaluate 3) Evaluate

4) Evaluate 5) Evaluate

Properties of definite integrals I) If is defined at x = a, then II) If is integratable on [a,b], then III) If is integratable on three closed intervals determined by a, b, and c, then

Properties continued IV) If is an even function (recall f(x) = f(-x), all exponents are even, symmetric with the y- axis) then V) If is an odd function (recall f(-x) = -f(x), all exponents are odd, symmetric with the origin) then

6) Given Find a) b) c) d)

7) Evaluate

8) Evaluate

9) Evaluate

Homework Worksheet 4-2A and Page 278 # 33, 34, 35, 36, 38, 40, 41, 42 and 43 using the given values