The trapezoidal approximation will be the average of the left- and right-endpoint approximations.
Let's consider a simple example of estimating the value of a general definite integral,
Split up the interval
into
equal subintervals,
where
and
. Each subinterval has measure (width)
.
Now denote the left- and right-endpoint approximations by
and
, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are
. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints,
.
So, you have
Now let
denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,
Factoring out
and regrouping the terms, you have
which is equivalent to
and is the average of
and
.
So the trapezoidal approximation for your problem should be
How many three-fourths are in 2? 2 complete sets of three-fourths can be made and 2 of the 3 pieces need to make \frac34 are left over, so we have another \frac23 of a three-fourths. and we can see that there are 2 wholes with 4 fourths in each whole, so there are 2\times 4 fourths in 2.
Answer:
123
Step-by-step explanation: