# Thread: Ways to Estimate Area under A Curve?

1. ## Ways to Estimate Area under A Curve?

Besides Riemman sums and the substitution method, how can i estimate the area under the curve for these problems? I was able to find the area using the substitution method, but my TA mentioned how there is a quicker way to estimate the area . He said something about drawing a box, and he used inequalities to represent the area?

Also, i heard that all the areas are equal and that they are equal to 2.

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https://imgur.com/a/9K1rw

2. ## Re: Ways to Estimate Area under A Curve?

I don't know what your TA has in mind but for a quick back of the envelop estimate I'd just treat them all as triangles.

I don't see how estimates will help you solve this problem though. It wants to know which areas are exactly equal.

3. ## Re: Ways to Estimate Area under A Curve?

If you're looking at an approximation to a definite integral you might want to look-up Simpsons Rule, Trapezium Rule ...

4. ## Re: Ways to Estimate Area under A Curve?

The estimation needed in this problem has a very simple geometric idea: if you have a nonnegative function f(x)f(x) on an integral [a,b][a,b] and you want to estimate ∫baf(x)dx∫abf(x)dx, you can draw a rectangle of width b−ab−a and height MM where MM is bigger than f(x)f(x) for all x∈[a,b]x∈[a,b] around the graph on the interval to get an upper estimate on the integral (in your workshop writeup, you have to indicate where and how you use this; alternatively you can argue using monotonicity of the function and Riemann sums).

this is what he msged me

5. ## Re: Ways to Estimate Area under A Curve?

i was able to find the areas for 3 of them using substitution but i cant seem to use substitute for the bottom right problem.

Nevermind! I think i can use area of a triangle!
I got a really smaller number: 0.06. I thought the would all be equal to 2 cause that's what i heard during class? Maybe they're wrong?
nvmd, it looks wrong! can someone help?