Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #26 20120425 17:13:25
Re: Calculus  Area of a curve
You are not integrating between the two crossing points on the x axis. Integration theory works out areas between two ordinates. Drive those little areas from your mind completely.
If you ask, I'll go through the 'why' for you. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #27 20120425 17:24:47
Re: Calculus  Area of a curveOh,yes.I forgot that! Ok,thanks for the clarification,K5. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #29 20120425 19:46:04
Re: Calculus  Area of a curveHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #30 20120425 22:02:07
Re: Calculus  Area of a curvehi amberzak and Stefy, So F is made by just summing the areas of all the infinitely thin rectangles with height f(x) and width dx. Now, on the f(x) graph I have shaded an area in yellowy orange to indicate the area under f up to a vertical line x. Then I have added a thin strip in red , width h (delta x) , for the next little bit of area to be added. I've used h on the diagram because getting a delta x is a bit tricky on this diagram. So how big is this extra area? Well it is smaller than a rectangle width h and height f(x+h). And it is bigger than a rectangle width h and height f(x) Thus or so so let delta x tend to zero so the differential gets sandwiched between two values that approach each other and in the limit So differentiation is the reverse of integration. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #31 20120426 02:43:14
Re: Calculus  Area of a curveShouldn't it be less than or equal to in the inequalities? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #33 20120426 04:08:58
Re: Calculus  Area of a curve
Yes it should. And the diagram only works when f is increasing ..... so it's not a fully rigorous proof. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #34 20120426 05:10:33
Re: Calculus  Area of a curveHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 