Why is Trapezoidal so called
since we can approximates the given integral by the sum of n Trapezoids
both (1) and (2)
None of the above
since we can exact the given integral by the sum of n Trapezoidal
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Step-by-step explanation:
We know from a previous lesson that we can use Riemann Sums to evaluate a definite integral
b
∫
a
f
(
x
)
d
x
.
Riemann Sums use rectangles to approximate the area under a curve.
Another useful integration rule is the Trapezoidal Rule. Under this rule, the area under a curve is evaluated by dividing the total area into little trapezoids rather than rectangles.
Let
f
(
x
)
be continuous on
[
a
,
b
]
.
We partition the interval
[
a
,
b
]
into
n
equal subintervals, each of width
Δ
x
=
b
−
a
n
,
such that
a
=
=
b
.
Trapezoidal Rule Concept
Figure 1.
The Trapezoidal Rule for approximating
b
∫
a
f
(
x
)
d
x
is given by
b
∫
a
,
the right-hand side of the expression approaches the definite integra
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