# 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

Consider the region below ​above the​ x-axis, and between

Let ${x}_{i}$ 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

Step 1
We have to estimate ${\int }_{0}^{6}\left(6-x\right)dx$ by using the mid−point ruleusing six sub−interval.length of sub−interval

Therefore,the sub−intervals consists of
The mid−point of these sub−intervals are
Thus,

$=18$
hence, the approximated area