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

\(f(x)=x^2+1\) is increasing on the interval. so "inscribed" rectangles will have the height of the left hand endpoint of the intervals

Answer 2

if you break up the interval \([2,4]\) in to four parts, they will be at \(2,2.5,3,3.5,4\) each will have length \(.5\)

Answer 3

your job is to compute
\[f(2)\times .5+f(2.5)\times .5+f(3)\times .5+f(3.5)\times .5\]
\[(f(2)+f(2.5)+f(3)+f(3.5))\times .5\]

Answer 4

would it be 17.75?