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### Course: Class 12 math (India)>Unit 9

Lesson 2: Indefinite integrals intro

# Graphs of indefinite integrals

More practice identifying the graph of the antiderivative of a function.

## Want to join the conversation?

• Has Sal done videos on transformations of graph? I mean when do we shift the graph, when do we scale up/down the graph etc?

Can anyone, please provide the link to understand this concept of scaling/shifting the graph?
• why there is dx in the expression, and also what is it for.?
• In the case of integrals, the dx tells us what our variable of integration will be; in this case, we're integrating with respect to x. More generally, the dx is a "differential element of x", which represents an infinitesimal, near-0 change in the value of x.

Right now, you've probably only seen integrals with one variable, but as you get further into calculus, you'll come across things like u-substitution and multiple integrals where it's important to define which variable will be used for the integration.

Lastly, if you're curious: although this isn't rigorous, we can think about differentials this way. Say you have a function f and its derivative df/dx (that's the Leibniz notation for derivatives, which looks like a fraction and can be useful for visualizing operations like this "algebraically"). If we want to find the antiderivative of df/dx, we need to sum up all of the infinitesimal changes in f -- in other words, we need to find the sum of all of the dfs. So we say that df/dx = df/dx (that's just an identity), then we multiply through by dx to get df = (df/dx) dx. Then by integrating both sides, we get int()df = f = int(df/dx) dx.

I hope you find some of that helpful.
• Hello, sorry but I do not understand yet. Why did you not chose D?
• I think that he didn't choose the answer "D" because it is supposed to be connected to the "y" part of the graph and that one is not centered in the graph. So it would not be directly on top of the line of "y"