The Net Change The net change =.

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Presentation transcript:

The Net Change The net change =

The Net Change The net change =

1 2 1 MATH-101 MATH-102 MEAN VALUE THEOREM FOR DEFINITE INTEGRALS there is at least one number c in (a, b) 1 f(x) is continuous on [a, b] 2 f(x) is differentiable on (a, b) MATH-102 MEAN VALUE THEOREM FOR DEFINITE INTEGRALS at some point c in (a, b) 1 f(x) is continuous on [a, b]

1 MEAN VALUE THEOREM FOR DEFINITE INTEGRALS at some point c in (a, b) 1 f(x) is continuous on [a, b]

The Definite Integral EXAM-1 TERM-102

THE DEFINITE INTEGRAL Term-092

THE DEFINITE INTEGRAL Term-092

THE DEFINITE INTEGRAL Term-082

Term-092

THE DEFINITE INTEGRAL Term-103

DEFINITION

TERM-091

TERM-082

TERM-082

INDEFINITE INTEGRALS TERM-092

INDEFINITE INTEGRALS

THE SUBSTITUTION RULE T-102

THE SUBSTITUTION RULE 092

THE SUBSTITUTION RULE 082

THE SUBSTITUTION RULE 092

THE SUBSTITUTION RULE Find Find

Even and Odd Term-102

Even and Odd Term-102

Even and Odd

Types of Discontinuities. Continuity Types of Discontinuities. removable discontinuity infinite discontinuity jump discontinuity

Integrabel Function Differentiable integrable Continuous

Integrabel Function integrable Continuous integrable number of removable and jump discontinuities are finite

Integrabel Function integrable number of removable and jump discontinuities are finite integrable

Integrabel Function number of removable and jump discontinuities are finite integrable For integrability to fail, a function needs to be sufficiently discontinuous that the region between its graph and the x-axis cannot be approximated well by increasingly thin rectangles. EXAMPLE: