Given f(x)=2x2-5, write the summation equation for A(f, 2 ≤ x ≤ 6) using 5 right endpoint rectangles.

Answer 1

A = lw, right? Remember that the y-value is how "tall" our function is at each x-value.

With a difference of 4, 5 triangles are 4/5 = 0.8 each. Since we are talking about right endpoint rectangles, the area of the first rectangle is 0.8(f(2.8)), etc.

A = 0.8(f(2.8)) + 0.8(f(3.6)) + 0.8(f(4.4)) + 0.8(f(5.2)) + 0.8(f(6))

We can factor out the 0.8...

A = 0.8(f(2.8) + f(3.6)...

If we had the same with left endpoints, we'd have f(2), f(2.8)...f(5.2).

Hope this helps!