Consider the region below f( x ) = ( 6 − x ),above the x-axis, and between x = 0 and x = 6. Let x_{i} be the midpoint of the i th subinterval. Approxi

Ava-May Nelson 2021-01-07 Answered

Consider the region below ​f(x)=(6 x),above the​ x-axis, and between
x=0 and x=6.
Let xi be the midpoint of the i th subinterval.
Approximate the area of the region using six rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately how many square units?

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saiyansruleA
Answered 2021-01-08 Author has 110 answers

Step 1
We have to estimate 06(6x)dx by using the mid−point ruleusing six sub−interval.length of sub−interval
Δ x=6  06=1.
Therefore,the sub−intervals consists of [0, 1], [1, 2], [2, 3], [3, 4], [4, 5] and [5, 6].
The mid−point of these sub−intervals are {12, 32, 52, 72, 92, 112}.
Thus,
M6=1. f(12) + 1. f(32) + 1. f(52) + 1. f(72) + 1. f(92) + 1. f(112)=11/2+9/2+7/2+5/2+3/2+1/2
=18
hence, the approximated area 06 (6  x)  18unit2.

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