What is Antiderivative: Definition and 177 Discussions
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite operation is called differentiation, which is the process of finding a derivative. Antiderivatives are often denoted by capital Roman letters such as F and G.Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.
In physics, antiderivatives arise in the context of rectilinear motion (e.g., in explaining the relationship between position, velocity and acceleration). The discrete equivalent of the notion of antiderivative is antidifference.
I used to be able to do stuff like this when i was in high school but now I am in college and i can't do basic stuff like this. the problem this sub problem is from is
Find the volume of the solid formed by rotating the region enclosed by
y=e^{ x} + 5, \ y=0, \ x=0, \ x=0.1
Im trying to...
Wow, I totally forgot how to do these.
I have a graph of a line, but it does not say the function. I have to sketch the antiderivative.
Does anyone have any links or advice to start me out.
TIA
my retarded textbook has this question i need the antiderivate of e^xsquared
and i hav no idea. thanks
ps. should this be in the calculus forum?
i don't really know what calc is?
Antiderivative of this? - kinematics
a kinematics question
v = 1 + e^x
find x in terms of t given that x = 0 when t = 0
what i did:
dx/dt = 1 + e^x
dt/dx = 1/ (1+ e^x)
so t = the antiderivative of 1/(1+ e^x)
i tried and i kinda did this...
loge(1 + e^x)/e^x + cbut it doesn't seem right
My AP calculus course has just started integration and so on. Because the exam date does not match up with my school's schedule, I'm kind of learning all of this in a disjointed manner at a faster rate than a normal class...
I'm staring at this question, and am drawing a blank:
find the...
If f is the function defined by f(x) = (x^2 + 4x)^(1/3) and g is an antiderivative of f such that g(5) = 7 then g(1) =
I thought that I need to find the antiderivative of f but it turns out that it's really messy so I'm not sure, is there something I'm missing to be able to solve for g(1)?
What does the antiderivative of a distance versus time graph represent? What does the antiderivative of the anitiderivative of a distance versus time graph represent? I think the units would be meters multiplied by seconds. Thanks.
What is the antiderivative of earctan(x)?
I can't seen to find this anywhere, although I suspect the answer would be pretty easy. This is the first problem of the first assignment in Calc 2. It is suposed to be review from Calc 1, but I can't figure it out. :grumpy: :yuck: :cry:
Problem states:
Find and antiderivative F of f(x)=x^2\sin(x^2) such that F(1)=0.
I thought at first that I would use u=x^2 to simplify the matter but I don't seem to get anywhere. I can't seem to figure out a way to start it off either...I was considering the Squeeze Theorem because they...
Anyone know how to get antiderivative of these? I am stuck.
1) cos(t^5)
2) tan(x^2)
3) (1-x^2)^(1/3)
Any explanation on how to do these would be appreciated.
Finding the antiderivative for fractions?
Hello,
I get antiderivatives and the idea behind them. But I still don't really comprehend how to apply it towards a fraction.
We know that \int (\frac{1}{x}) dx = ln|x|
So would the antiderivative of \int (\frac{4}{x}) dx = 4(ln x) ?
But...
[SOLVED] Simple Antiderivative
How would I compute the antiderivative of
\int \sqrt{1-\frac{x^2}{2}}
It looks familiar, but I can't quite remember how...
How would you guys come about getting the antiderivative for the following function?
8u^5 / ((4 + u^4)^2)
I tried rearranging the equation like the following:
8u^5 * ((4 + u^4)^(-2)), but it's not really getting me anywhere. I tried to do a u substitution, but can't find one where it...
The title sums it up. How can I find this?
\int \frac{dx}{x^2 \sqrt{1+x^2}}
I've tried a lot of different things to come up with an answer. My answers must be wrong, but I don't see where I'm making a mistake. Here's one way I've tried to solve the problem:
Let
u = (1+x^2)^{-1/2}
v =...
The general idea I have in mind when it comes to analyzing a graph that has a derivative f and its antiderivative F (\mathrm{C}=0) is the following:
- When f is positive, F increases.
- When f is negative, F decreases.
However, I came across a couple of problems in my textbook that don't...
I have two quick questions. The first is, if a ball is thrown from a bridge 25 meter above the ground at 49m/s, is the acceleration negative? I thought since it was thrown up, it would be positive, but the book has a similar problem, a ball is thrown upward at a speed of 48ft/s from a cliff...
Does anyone know of a good, preferably flash or html-based antiderivative calculator? I'm on a Mac and can't run any windows executable file.
https://www.symbolab.com/solver/antiderivative-calculator
And if not, would someone please tell me the antiderivative of tan?
[edit]
I'll just give the...
Well, I'm working on a project, but I've run into a bit of a snag: an antiderivative that I need to evaluate, but can't. Even Mathematica's stuck on this one. :) Here it is:
\int \frac{dx}{2+cos(ax)-cos(\frac{b}{x})}
Any help would be appreciated, even if a numerical approximation is all...
Need Help With Antiderivative Problem!
We've put 3 people's minds to this, and every time we end up with 2 non-equal constants having to be equal for the equation to be true. Give it a whirl, b/c I have nothing left to lose... my dignity has already been shot by now.
Okay, here's the deal...
is it true or false that all real function is an antiderivative of some real function but neither real function have an antiderivative?
I still have the doubt!
Definition(Louis Leithold,The Calculus with Analytic Geometry)
Antiderivative: F is antiderivative of f in I if F'(x)=f(x) for...