Question

Estimate the area of the given function, f(x) = x2 + 1 using 4 inscribed rectangles on the interval [2, 4].

Note: inscribed rectangles lie inside the region

Answer 1

Split the domain [2,4] into 4 equal parts. (4-2)/4 = 2/4 = 0.5
Draw 4 rectangles. The width of each rectangle will be 0.5.
The height of the rectangle will depend on whether we choose the upper endpoint or the lower endpoint. Instead let us choose the middle point.
So our rectangles heights are at x = 2, 2.5, 3, 3.5, 4.0
Choose the midpoints in each interval: 2.25, 2.75, 3.25, 3.75

Evaluate f(x) at x = 2.25, 2.75, 3.25, 3.75.
Multiply each height by 0.5 to get an estimate of the area of each rectangles. Add them up to find the total area.

Answer 2

Thank you so much