Approximate the area under the curve on the given interval using rectangles and midpoint evaluation. Round to three decimal places. on ,

Question

Approximate the area under the curve on the given interval using  rectangles and midpoint evaluation. Round to three decimal places.  on  ,

Quizplus · Accepted Answer

We can start by dividing the interval [0,4] into 11 equal subintervals, each with width Δx = (4-0)/11 = 0.3636 (rounded to 4 decimal places).
Then, we can use the midpoint of each subinterval as the x-coordinate of the rectangle, and evaluate the function at that point to get the height of the rectangle.
For example, the height of the rectangle with midpoint x=0.3636 is f(0.3636) = 0.2865 (rounded to 4 decimal places).
Using this method, we can calculate the height of each rectangle and add up their areas to approximate the area under the curve.
The sum of the areas of the 11 rectangles is approximately 1.145 (rounded to 3 decimal places).
Therefore, the correct choice is C.

Approximate the Area Under the Curve on the Given Interval