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.
-$$f ( x ) = 2 x + 3 \text { from } x = 0 \text { to } x = 2 ; n = 4$$
A) 11
B) 13
C) 17
D) 15

Question

Quizplus · Accepted Answer

The width of each rectangle is (2-0)/4 = 0.5. The heights of the rectangles are f(0.5) = 5, f(1) = 5, f(1.5) = 7, and f(2) = 7. The area of each rectangle is (0.5)(5) = 2.5, (0.5)(5) = 2.5, (0.5)(7) = 3.5, and (0.5)(7) = 3.5. The total area is 2.5 + 2.5 + 3.5 + 3.5 = 11.

Approximate the Area Under the Curve and Above the X-Axis f(x)=2x+3 from x=0 to x=2;n=4f ( x ) = 2 x + 3 \text { from } x = 0 \text { to } x = 2 ; n = 4f(x)=2x+3 from x=0 to x=2;n=4

Approximate the Area Under the Curve and Above the X-Axis $f ( x ) = 2 x + 3 \text { from } x = 0 \text { to } x = 2 ; n = 4$