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## Integral Calculus

### Course: Integral Calculus>Unit 1

Lesson 9: Fundamental theorem of calculus and definite integrals

# Antiderivatives and indefinite integrals

AP.CALC:
FUN‑6 (EU)
,
FUN‑6.B (LO)
,
FUN‑6.B.1 (EK)
,
FUN‑6.B.2 (EK)
,
FUN‑6.B.3 (EK)
What's the opposite of a derivative?  It's something called the "indefinite integral". Created by Sal Khan.

## Want to join the conversation?

• So, is it all about writing "possible functions" from its derivatives?
• Well, essentially.

In application, you'll have additional constraints, which will narrow down the possibilities.
• How can we use derivatives, integrals and anti-derivatives in real life situations or in an occupation like engineering? I'm kinda confused here, if anyone can give an example and a detailed explanation I would really appreciate it. I really want to understand this intuitively. Thanks in advance!
• Okay after studying so far I understand that:
derivatives are used to find the minimum or maximum of something to optimize something.
• Are their any good websites that provide integration problems?
• I'm currently in Grade 10, and our math subjects are mainly on trigonometry, quadratic equations, and general algebra 2 stuff. I can safely say that I've learnt all Grade 10, 11 and even 12 math level subjects with Khan Academy since I am so fascinated by math. I was wondering whether I should start learning calculus since it's so profound and deep. Should I just wait it out till college or can I start learning this by myself?
• Start now!
Start here at the beginning of the Pre Calculus Track: https://www.khanacademy.org/math/precalculus
Do the work in the order presented - if you don't get one or two things, ask a question.
If you are not getting a lot of things, best do some appropriate review.
Have Fun!
• cant the anti derivative of 2x be x^2+c1+c2+...+cn ?
is it so that all the constants are summed and they become one constant?
Which gives us just one constant notation c?
Have I understood correctly?
• Yes, that is correct. That will be a useful understanding when you are solving differential equations, which will depend heavily on those arbitrary constant.
• Will there be videos about solving rational,irrational and hyperbolic function integrals?
• What is the range of points that you need an area for?
• In the integral notation, why is there a dx at the end? I've looked everywhere for an explanation, but I just can't find one. I would really appreciate an answer.
• The symbol dx has different interpretations depending on the theory being used. In Leibniz's notation, dx is interpreted as an infinitesimal change in x and his integration notation is the most common one in use today. If the underlying theory of integration is not important, dx can be seen as strictly a notation indicating that x is a dummy variable of integration; if the integral is seen as a Riemann integral, dx indicates that the sum is over subintervals in the domain of x; in a Riemann–Stieltjes integral, it indicates the weight applied to a subinterval in the sum; in Lebesgue integration and its extensions, dx is a measure, a type of function which assigns sizes to sets; in non-standard analysis, it is an infinitesimal; and in the theory of differentiable manifolds, it is often a differential form, a quantity which assigns numbers to tangent vectors. Depending on the situation, the notation may vary slightly to capture the important features of the situation. For instance, when integrating a variable x with respect to a measure μ, the notation dμ(x) is sometimes used to emphasize the dependence on x. Source: http://en.wikipedia.org/wiki/Integral#Terminology_and_notation
• is this calculus 2 material?
• Calc 1 should include at the very least a brief lesson on this. Calc 2 goes much farther in-depth with integrals.
• What will be the derivative of :
Squareroot of ax.
a being a constant does it effect the derivation.
naive in maths
• Power Rule states ax^1/2 = (1/2)ax^((1/2)-1) = (1/2)ax^(-1/2) = a/2x^1/2
(1 vote)
• If a Derivative shows the rate of change of a curve & if an Integral shows the area under the curve.

Then what is an Antiderivative? What is it used for?