Area under graph. Conceptual Doubt.

[candid tapir]

(Refer to the first attachment for the question)

[leaden basin]

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[fringe saddle]

I assume you mean f'(x) is the function describing the graph.

[candid tapir]

Yes yes..

[fringe saddle]

Then it's inaccurate to state that the heights are f(a) and f(b).

[candid tapir]

ofh... wait lemme rethink

wait. If i say f(x) is the equation of graph

will it be correct saying that integral of f ' (x) will be f(a) - f(b)

[fringe saddle]

...yes, but then it's not the area under the curve f.

It's the area under f'.

[candid tapir]

so you mean that the equation i have put forward will give area under f ' (x)

right?

[fringe saddle]

The integral will.

[candid tapir]

hmm.. my sir gave it to me
and i am really confued rn :\

I knew area under the grpah and how to solve its problems
but conceptually i am strugglin g

[fringe saddle]

The difference in height of the graph of a function at two points gives the area under the graph of the derivative of the function between those two points.

[pliant thicket]

this is graph of function f(x) but if u draw out the graph of f'(x) then mathematically the are will come out to be the height difference

The are is related to the graph f ' (x) while the hieght differnce being meausred is of graph f (x) so its pretty hard to think intuitively

[candid tapir]

I was trying to establish a correlation

so... needed some creative minds to come on board who could give something similar on basis of their in-depth knowledge in calculus.

cz i am just a rookie 😐

[pliant thicket]

ohh i dont know the corelation

ig techie would be able to help better