Antiderivative Definition and 177 Threads

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. :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...

does anybody know the antiderivative of 1/(sqrt(lnx - (a constant))

I'm trying to find the antiderivative of [sec(2x)tan(2x)], I can't figure out what part I should be substituting. Any help is appreciated. Thanks, hk

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...

Do you guys have any tips on how to get the antiderivative of 1 / (x^2 - 1)? Thanks.

Find all possible functions with the derivative f'(x) = 4x^2 - 3 + \sin x Is this right: \frac {4x^3}{3} - 3x - \cos x + C ? Thanks

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...

Why does the antiderivative give us the area? I can't really find it in textbooks.

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...

how do I find to antiderivative of: x((2x^2) - 2)^3

can anyone help me find an antiderivative for (x^2)((9-(x^2))^(1/2))

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...