Definite Integral and
the Fundamental Theorem of Calculus
Definition of Definite Integral If f is defined on the closed interval [a, b] and the limit of Riemann sums over the partitions ᅀ exists,
then f is said to be integrable on [a, b] and the limit denoted by
The limit is called the definite integral of f from a to b. The number a is the lower limit of integration and the number b is the upper limit of integration.
Properties of Definite Integrals
EXAMPLE 1
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**RECORD THIS IN YOUR PINK SHEET!
Example 1
taketheantiderivative 2keepthelimitsofintegration IgX3 3 x
I
Evaluatetheantigeminmeyngaumoenniang 213 312 Ill 3111hmOfCSabfaddx Fla Fla 8
3 6 Ig f 3 Y y2 3
andthen asimplify
Iz 3 Iz za µs
Iz IEEE.eesnretsneneEotTeaana9ne
sneyeainIs ii
3 theyaxis
Example 2 tieRewriteso
iiiinertia 3fix'tDXtaketheMTderivativesina.si it 3 fExZ 2X
vmaideariemmeiat 21452 2 1 3andaccordingto thendamental1hmCalabfaddxFcbFca I 6 2simplify 4
Example 3