Area Under a Curve

1
Riemann Sums

• Area Under a Curve

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Riemann Sum
3
f(x)
b
a
4
Left-Hand Endpoint
5
f(x)
b
a
6
Right-Hand Endpoint
7
f(x)
b
a
8
Midpoint
9
f(x)
b
a
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Trapezoids
11
The Definite Integral
Integrand
Limits of Integration
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The Definite Integral
If f(x) is continuous over a,b,
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If f(x) gt0 then the area under the curve is
equal to the definite integral
f(x)
a
b
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If f(x) lt0 then the area enclosed by the curve
is equal to the definite integral
b
a
f(x)
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Properties of Definite Integrals
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Properties of Definite Integrals
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Properties of Definite Integrals
Note It is not necessary that a lt b lt c !