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## Main Question or Discussion Point

**Studying integrals....**

I am studying for my maths B exam that is coming up and may need some help in understanding some concepts.

Here is one question that i was getting some practise on but i got the wrong answer !!

Q: The area under the curve

*x*²+ 1 between 1 and 4 is approximated by left rectangles of width 1 unit. What is the total area of the aproximation?

A: Well I calculated the area using the fundamental theorem of calculus and I ended up with 24...but the answer was wrong it turned out to be 17 according to BOB. I then remember that the fundamental theorem of calculus give you the exact area not the aproximated area. I am not so sure about how to get the approximated area though. Is there a formula or something I can use?

I know that the x and y values I am interested in are as follows (0, 1), (1, 2), (2, 3) and (3, 4). I am trying to find the area under the curve at these points. I drew in the rectangles under the curve and found the area but I got a value of 10 :grumpy:. Nothing is working for me at the moment so I need help...I really did think that that would work but of course 1 + 2 + 3 + 4 = 10 . But i haven't tried making the rectangles in smaller subdivisions yet so maybe thats what I have to do...and if anyone knows a formular or an easier way please tell me!

Well I'll try the smaller subdivision thing now and see if I get 17....and if I don't i'll be a little , but if someone has an easier way or some kind of formula i'll be