Question

Approximate the area under the curve y = x^2 + 1 from x = 2 to x = 5 using a left sum with 6 subdivisions

The area is approximately=

PS. its supposed to be a whole number, when I tried entering an equation I got it wrong.

Answer 1

I recall oobleck doing this for you ..... ??

you have 6 rectangles, each one of width (5-2)/6 = 0.5 or 1/2
the height of the first rectangle is f(2) = 2^2 + 1 = 5
the height of the 2nd rectangle is f(2.5) = 2.5^2 + 1 = 7.25
.....
the height of the 6th rectangle is f(4.5) = 4.5^2 + 1 = 21.25

now add:
(1/2)(5) + (1/2)(7.25) + ... + (1/2)(21.25)
= (1.2)(5 + 7.25 + ... + 21.25)

surely you can do this arithmetic, right?

btw, this does NOT turn out to be a whole number, but the actual area using Calculus does work out to be exactly 42

Check the wording of the question.