MAT 212 Brief Calculus

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MAT 212Brief Calculus

• Section 5.4The Definite Integral

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If f is continuous on the interval a,b, and
f(x) F (x), then To find
, first find F, then calculate F(b) -
F(a) This method of computing definite integrals
gives an exact answer.
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Examples
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Notation for the general antiderivative of a
function f(x) looks like the definite integral
without the limits of integration.
Definite General
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This gives you a number
Definite General
This represents a family of functions
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The Definite Integral If a, b, and c are any
numbers and f is a continuous function, then
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The Definite Integral Let f and g be continuous
functions and let c be a constant, then
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Find the exact value of the area between by the
graphs of y e x 3 and y x 2 for 0
x 2
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Find the exact value of the area between by the
graphs of y x 1 and y 7 - x for 0 x
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Find the exact value of the area enclosed by
the graphs of y x2 and y 2 - x2 Lets
look at 13 from the book