What is the role of "Approximation and refine" in both differential and integral calculus?
Q. I need help on my calculus...It says to " Discuss the role of "Approximation and refine" in both differential and integral calculus. Provide two examples..." If differential calc is finding the slope of a specific point along a curve and integral calc is the opposite...finding the area between the curve and the X-axis...I just dont get it! Please someone help!
Asked by casey - Tue Dec 11 19:25:23 2007 - - 1 Answers - 0 Comments

A. One way to think about "taking a limit" is as the ultimate step in a series of refinements. E.g., if you are taking the limit as h -> 0, you can think of this as taking smaller and smaller and smaller values of h. (Indeed, if you take a more advanced course, you will see that the epsilon-delta definition of a limit is equivalent to considering all sequences that converge to the point. But that can wait a couple years!) So, if you think back to how you constructed the definition of derivative, it was by taking a secant line and letting the horizontal length go to zero. For integrals, you sliced a region into a bunch of little wedges (rectangles or trapezoids, most likely), and let the width of the wedges go to zero. In each case, you're [cont.]
Answered by jeredwm - Tue Dec 11 19:48:09 2007

Does anybody know what is the application of Integral calculus and differential calculus?
Q. Can anybody tell me where integral calculus and differential calculus in everyday life apply practically? Is it only restricted to integrating sin^6X , e^X^2 like stuff ? How can u make it more interesting practically in our everday life ?
Asked by tormentor of ssouls - Tue Dec 26 04:18:11 2006 - - 5 Answers - 0 Comments

A. I use it every day when I calculate the health of a patients' kidneys, liver, stomach, or any organ that functions. How fast the kidney uptakes and excretes radioisotopes tells me if someone is ok, in trouble, or may get very sick. Referring doctors and patients thank me every day for saving their lives. I also use it almost every day when I analyze the markets. There's no better incentive to learn how to use math than realizing that you can make $$ doing it! Whoever figures out the secret formula that can predict market behavior, wins! And calculus gives me a huge edge over run-of-the-mill loser day-traders. To your success with numbers! If you know how to read numbers, you can always tell if someone is lying to you. That's power! [cont.]
Answered by DavID - Tue Dec 26 04:32:42 2006

How can I include a Calculus Integral symbol in my paper?
Q. I need to email my professor a Calculus project, so I can't hand write in the Integral symbol. How/where can I get the integral symbol (the elongated script capital S) to include in my paper?
Asked by jennuinelove - Thu Dec 20 11:18:47 2007 - - 5 Answers - 0 Comments

A. You could just copy and paste it from Word. You may need to use the rich text format in your email.
Answered by Dr D - Thu Dec 20 11:29:35 2007

why do you have to learn integral calculus?
Q. why do you have to learn integral calculus to find out the volume of irregular solids if you can just use the displacement of water with a graduated cylinder? its so much easier
Asked by Adidas - Mon Mar 24 03:17:00 2008 - - 5 Answers - 0 Comments

A. Practically in real world first theoritically things are calculated and then put into practical For example if you want to prepare some shape with gold you have to know the volume of it.There is no object in the starting to test with water.we first calculate it theoretically prepare the object then we can verify the volume with water displacement Another problem is error however accurate u may be some error will be thr in physical measurement.
Answered by Maheedhar - Mon Mar 24 03:37:35 2008

Does Differentiation means Differential Calculus and Integration means Integral Calculus?
Q. Please tell what are the topics coming under Differential & Integral Calculus? A list is required Thankxxx.
Asked by Holyspirit - Wed Apr 8 04:53:47 2009 - - 3 Answers - 0 Comments

A. Differential calculus is mostly the material you cover in calc 1. You're introduced to the limit, the definition of the derivative, taking the derivative of a function, and techniques/rules for taking the derivative of a function. Toward the end you are introduced to the fundamental theorem of calculus, which basically says: F'(x) = f(x) F(x) is the antiderivative of f(x). If you take the derivative of the antiderivative, the theorem says you will end up with your original function. You are then introduced to basic techniques of integration based on what you know about differentiation. You are also introduced to various applications of integrals (antiderivatives). For example, if you wanted to find the area under the curve of f(x)=x [cont.]
Answered by 308 - Sat Apr 11 14:42:19 2009

How to learn Integral Calculus the easy way?
Q. I'm a 12th grader, and I can't seem to follow Calculus at all. What is the easiest way to understand it free of cost? any online resources? any tips?
Asked by Avi Arun - Sun Oct 11 12:08:12 2009 - - 3 Answers - 0 Comments

Is the mean value theorem of integral Calculus valid if f is not continuous?
Q. Suppose the real valued function f is Riemann integrable, but not continuous, over [a,b]. Then, does there exist some c in (a,b) such that f(c) = [Integral (a^b)f(x) dx]/(b -a)? I tried to prove this based on the fact that the set of discontinuities of f in [a,b] has Lebesgue measue 0, but couldn't come to a conclusion yet.
Asked by Steiner - Wed Sep 12 15:50:29 2007 - - 1 Answers - 0 Comments

A. No. Consider the function f defined on [0, 1] by f(x) = 0, if 0 <= x < 1/2 f(x) = 1, if 1/2 <= x <= 1. Then the average value of f(x) on the interval [0, 1] is 1/2 (that is, [Integral (0^1)f(x)dx]/(1 - 0) = 1/2), but the function f does not assume the value 1/2 at any point in (0, 1). --- I am pretty sure, however, that if a real valued function f is Riemann integrable on [a, b], and has the intermediate value property on [a, b] (that is, if f(x) < c < f(y) for x, y in [a, b], then there is a z between x and y such that f(z) = c), then the Mean Value Theorem does hold. (This is a more general condition than continuity; continuous functions always assume intermediate values, but functions assuming intermediate values are not… [cont.]
Answered by TheMathemagician - Wed Sep 12 15:57:50 2007

Evaluate the definite integral using the fundamental theorem of calculus?
Q. Evaluate the definite integral using the fundamental theorem of calculus. integral (6,5) ((d/dt)sqrt(3+5t^4))dt need at least 4 decimal places, or leave as an algebraic expression using square roots.
Asked by boseali21 - Tue Aug 25 08:23:45 2009 - - 3 Answers - 0 Comments

A. We have INT [ f ' (t) ] dt = f(t) + c. Then, if G(t) is the given primitive, then G(t) = sqrt( 3 + 5 t^4 ). Hence, the req'd value is = G(6) - G( 5) =...
Answered by Hemant - Tue Aug 25 08:42:08 2009

What is differential and integral calculus? please explain?
Q. Also explain what did Sir Isaac Newton invent in calculus for which he is so famous?
Asked by Holyspirit - Sat Jun 20 08:47:05 2009 - - 3 Answers - 0 Comments

A. differential you learn about derivatives and how to use them with math you know to gain new insight about functions. integral the same but with integrals and derivatives. Newton formalized symbolic calculus, but civilizations all over have been doing it for ages. :)
Answered by unknown - Sat Jun 20 08:53:25 2009

How to integrate? Math integral calculus 10 pts please urgent it's an emergency?
Q. I have a calculus exam tomorrow and i don't know how to integrate, specially using trigonometric functions as sine, coseine, tangent, etc. If someone could help I'd appreciate it a lot please I don't wanna fail and I'm desperate
Asked by valep8922 - Tue May 13 22:01:58 2008 - - 2 Answers - 0 Comments

A. Integrating is easy. If you have something that you're suppose to integrate you just have to add one to the degree and divide by that number. Like if you have 3^4 then it would be (3^5)/5. For trig problems there's just formulas you need to memorize. Try At the bottom of the page there are examples with detailed problems on how to integrate trig problems. Good luck!
Answered by oh_my_josh2002 - Tue May 13 22:14:46 2008

Can anybody help me with integral calculus?
Q. I need to find the equation of a curve that passes through the point (2, 5) and has the gradient 3x^2 + 2x - 4. Can somebody try and talk me through it please? :)
Asked by Lloyd - Tue Jun 16 14:05:00 2009 - - 1 Answers - 0 Comments

How do you solve this calculus integral problem?
Q. Which trigonometric substitution would be most useful in evaluating (25 + x^2) dx? a) x = 5 tan b) x = 5 sin c) x = 5 sec d) x = 25 tan e) x = 25 sec Please show the work you used to arrive at your answer.
Asked by joe k - Wed Apr 9 01:08:37 2008 - - 1 Answers - 0 Comments

A. a. 25+(5tan )^2 =25+25tan^2 =25(1+tan^2 ) =25(sec^2 ) so you will be taking the integral of that, which is simple.
Answered by Everlasting - Fri Apr 11 03:02:12 2008

Who can tell me, step by step, how exactly had Newton invented the integral calculus?
Q. Who can tell me, step by step, how exactly had Newton invented the integral calculus?
Asked by imreko - Mon Feb 11 03:23:50 2008 - - 2 Answers - 0 Comments

A. Well, like all math, you could argue that it wasn't "invented", Newton "discovered" it, like Liebnitz did. The initial idea is simple, define df/dx = the limit of [f(x+c) - f(x)]/c as c goes to zero. Form there you can do it in reverse to get the "fundamental theorem of calculus": The integral from a to b of df/dx = f(a) - f(b) Pretty much any textbook will take you through this. If you are interested particularly in how Newton viewed it, then simply read his text, the Principia.
Answered by supastremph - Mon Feb 11 03:53:48 2008

How do you do integral calculus in polar?
Q. How do you do integral calculus in polar?
Asked by CogitoErgoCogitoSum - Fri Sep 19 03:29:29 2008 - - 2 Answers - 0 Comments

A. Substitute: x=r*cos , y=r*sin , dx*dy=r*dr*d You need to find the limits of r and for the area of integration, too. The limits of are constants, while the limits of r could be constants or functions r=r( ).
Answered by rozeta53 - Sat Sep 20 07:06:57 2008

Can somebody help me with these calculus integral problems?
Q. Evaluate the following integrals: a) integral from 0 to sqrt(3)/3 of: 10/(t^2+1) dt b) integral from -3 to 3 of: e^(u+1) du c) integral from 3 to 4 of: (2+u^2)/(u^3) du
Asked by jeremy s - Thu Jan 24 00:47:21 2008 - - 1 Answers - 0 Comments

A. for a) you have to use a trig identity: integral of 1/(x^2+a^2)dt= (1/a) inverse tan(x/a) in this case a=1, x=t and 10 is a constant so it can be pulled to the front. answer = 10(inverse tan(sqrt(3)/3) - inverse tan((0) = 10(30 - o) = 300 b) integral of e^(u+1)du = e^(3+1) - e^(-3+1) =e^4 - e^(-2) =54.4628 c) you can break this question up. integral from 3 to 4 of (2/u^3)du + integral from 3 to 4 of (u^2/u^3) du = -1/u^2 + lnu (from 3 to 4) = [-1/4^2 + ln4] - [-1/3^2 + ln3] then simplify
Answered by J J - Thu Jan 24 01:11:47 2008

Can anyone help me with a Calculus definite integral problem?
Q. Could you please walk me through this equation... A particle starts at x=0 and moves along th ex axis with velocity equals v(t)=t^2+1 for t>0. Where is the particle at t=4. Approximate the area under the curve using four rectangles of equal width and heights determined by the midmpoints of the intervals. Thank you.
Asked by bluevolleyball12 - Mon Jan 21 20:11:49 2008 - - 1 Answers - 0 Comments

A. So first, integrate the velocity equation, as the intergral of velocity=distance. (1/3)t^3+t+c=x(t) x(0)=(1/3)0^3+0+c=0 c=0 x(4)=(1/3)4^3+4 x(4)=76/3 (this is the position it is at) The area under the curve of velocity, will also equal the position, as it is an accumulation of velocities. (It will not equal the total distance traveled, that would be the area under the curve of the distance equation). To do midpoint, A=(the width of the rectangles)(height of rectangle). So, A=(1)(v(1/2)+v(3/2)+v(5/2 )+v(7/2))=25
Answered by bbalcarl - Mon Jan 21 20:28:55 2008

Can you give me a good site where the integral calculus can be learned?
Q. Can you give me a good site where the integral calculus can be learned?
Asked by imreko - Sat Nov 1 03:56:06 2008 - - 3 Answers - 0 Comments

A. here is a good web site for integral calculus..
Answered by Engr. Ronald - Sat Nov 1 04:02:45 2008

Calculus Help? How to solve an integral with substitution?
Q. I'm just starting the second semester of calculus and feel like I'm lost - can anyone give me a general way to evaluate an indefinate integral with substition?
Asked by Corey - Mon Jan 21 19:50:28 2008 - - 1 Answers - 0 Comments

A. You can use substitution if one part of the expression to be integrated is the derivative (or a mulitple by a number) of another part. e.g. x sin(x^2 - 2) dx since d(x^2 -2)/dx = 2x, substitution is possible: u = x^2 - 2; du = 2x dx need the 2 in the original integral, so multiply by 2 (and 1/2 out front to make the net effect *1: 1/2 2x sin(x^2 - 2) dx = 1/2 sin u du = 1/2 (-cos u) + c = -1/2 cos (x^2 - 2) + c
Answered by Jennifer L - Mon Jan 21 20:12:09 2008

Why in the world is integral calculus so hard?!?
Q. Like I have to call my friend over and help with homework, and whatnot!
Asked by Tamahome - Wed Jan 23 16:25:43 2008 - - 2 Answers - 0 Comments

A. Basically you are finding the volume of a loaf of bread by taking an infinite number of slices which are infinitly thin and then adding the volume of all the slices. Calculus was originally an attempt to calculate the ratio of the diameter of a circle to its circumference. The perimeter of a polygon is the number of sides times the length of an individual side. A circle is a polygon with an infinite number of sides. This means the length of any side is infinitly small. Learning calculus is rather like learining algebra. There are a few basic rules and everything is simple after learning what they are. Calculus can be simple if only polynominals are involved. Basically, the integral of X^2 is 1/3X^3. Just raise the power by 1 and place… [cont.]
Answered by Roger S - Wed Jan 23 16:37:50 2008

What is an integral in a calculus equation which relates to physics?
Q. The equation I'm looking at is: Funny looking S thing, than p d V It's like this: ( p d V )
Asked by Sir Guitarist - Wed Nov 29 20:00:27 2006 - - 2 Answers - 0 Comments

A. The funny looking S thing is an integral sign, the p stands for pressure and the dV stands for a little change in volume. It sounds like the work performed by something expanding at constant pressure. The work is the amount of energy used.
Answered by Nicknamr - Wed Nov 29 20:05:09 2006