find area under the graph of f(x)=0.02x4−2.25x2+99 over the interval [6,10] by dividing the interval into 4 subintervals. Use the left endpoint of each subinterval.

Question

find area under graph of f(x)=0.02x4−2.25x2+99 over the interval [6,10] by dividing the interval into 4 subintervals. Use the left endpoint of each subinterval.

Answer 1

The 4 subintervals are [6,7], [7,8], [8,9], [9,10].

Instead of using calculus we can use the left endpoint as the height of a rectangle of unit width.

So the area is f(6)+f(7)+f(8)+f(9)=43.92+36.77+36.92+47.97=165.58.

(Using calculus the actual integral gives 176.896)