Choose the one alternative that best completes the statement or answers the question.
Approximate the area under the curve and above the x-axis using n rectangles. Let the height of each rectangle be given
by the value of the function at the right side of the rectangle.
-$$f ( x ) = 2 x ^ { 2 } + x + 3 \text { from } x = 0 \text { to } x = 6 ; n = 6$$
A) 200
B) 221
C) 211
D) 230

Question

Quizplus · Accepted Answer

The width of each rectangle is 1 (since the interval is 6 and n=6). The heights are calculated at x=1, 2, 3, 4, 5, 6. The sum of these heights gives the approximate area: f(1) + f(2) + f(3) + f(4) + f(5) + f(6) = 6 + 11 + 18 + 27 + 38 + 51 = 151. Multiply by the width (1) to get the area, which is approximately 221.

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