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1. Let f(x) be a continuous function that is defined for all real numbers x and that has the following properties:
(i) The integral from 1 to 3 of f(x)dx=(5/2)
(ii) The integral from 1 to 5 of f(x)dx=10
(a) Find the average (mean) value of f(x) over the closed interval [1,3].
(b) Find the value of the integral from 3 to 5 of [2f(x)+6]dx
(c) Given that f(x)=ax+b, find the values of a and b
2. Particle motion:acceleration, Particle motion:velocity, Particle motion:integration, Particle motion:ln, Particle motion:exp, Particle motion:position.
A particle moves along the x-axis in such a way that its acceleration at time t for t>0 is given by a(t)=(3/t^2). When t=1, the position of the particle is 6 and the velocity is 2.
(a) Write an equation for the velocity, v(t), of the particle for all t>0.
(b) Write an equation for the position, x(t), of the particle for all t>0.
(c) Find the position of the particle when t=e
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1) There's a formula for average value. I think it's 1/(bound 2 - bound 1) times (integral of stuff)
You know the integral from 3 to 5 is 10 - 5/2.
Combine this with the average value formula to get a) and b) (for b, do 2 times theintegral of f(x), then integrate 6 from 3 to 5)
1c) integral of f(x) = 1/2 ax^2 + bx + c = g(x)
g(3) - g(1) = 5/2, and g(5) - g(1) = 10, and g(5) - g(3) = 10 - 5/2.
Three equations, 3 unknown constants. You can solve that
2 a) the v(t) = integral a(t) dt. x(t) = integral v(t) dt.
Once you find a formula for v(t) and x(t) (don't forget the constants of integration), you can sub in v(1) = 2 and x(1) = 6 to find your constants
c) x(t) from part b --> x(e)
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wikipedia and maybe reading your textbook/paying attention in class helps a lot
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This isn't event that hard, if I can do it ANYONE should be able to do this. I can do it by hand, but the calculator does it in about 30 seconds. Graph the function and plug in the lower and upper limits and Tada your answer.
On April 22 2008 03:12 blabber wrote:
wikipedia and maybe reading your textbook/paying attention in class helps a lot
Yeah this helps also.
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Dude don't take the easy way out...as everyone has said...these problems are really easy. Do them.
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if you can't do these by yourself in these basic integrals and you plan to move on, you either need some serious tutoring or rethinking about what exactly it is you want to do.
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I probabaly do. I really do try to pay attention in class but half the time my mind is wandaring somewhere else becuz i don't understand what the fuk he's talking about. Seriously at least half the class doesn't have a clue wtf he's tlaking about and are passsing the class with C's. It's been like this the whole year and I seriously can't learn in his class becuz whenever i ask him a question he's always sarcastic. If i ask him a question and i answer something wrong, he jsut says "no" and just waits for me to give him the correct answer to which i dont know the answer to which is the reason why i called him to my desk in the first place to help me.
Sigh..maybe I should just get out of calculus if i can't even do this. Like i serioulsy don't even know how to start this. Word problems are so painful for me. I really really wanna learn this stuff but i dont know if its cuz im full kroean but the advanced level classes have always posed a problem whenever there was a word problem but worded "AP" style if u know what i mean. I mean if the question asks me to find the derivative of for example something like 6x^2 i can do that easily which is 12x. But word problems is seroulsy killing the fuk out of me T_T. I wanna learn and i know i have to do this myself if i want to learn but how can i start when i dont even know how to start.
Gah sorry this was so long and turned into a rant but this is pretty much my frustrattion i had with calculus the whole year t.t. The funny thing is, if someone good sits one on one with me i can learn eveyrthing easier but when it's the teacher talking in front of everyone, either my mind can't focus or i don't undersatnd wtf he's talking about. I just don't know what to do anymore.
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Does my post help at all? I don't like it when people straight out give you the entire solution.
As for the prof/tutor thing, it's really really hard teaching to an entire class as opposed to teaching one on one. For one, students are typically either shy or lazy and so they don't say anything, so you have no clue where the class is at. One on one, you have way more interaction and you can gauge easily where the guy is at in understanding.
As for understanding integrals, don't get caught up in calculations. If you really don't understand it, take a step back and ask yourself what each thing means physically. What is an integral? What is a derivative? If you can draw a picture and understand what each of these things are, you'll be a step closer toward understanding word problems. Word problems are no harder than straight up calculations. Just understand what it is you're doing when you're learning how to calculate stuff
As for the people saying that this stuff is easy and that he should reconsider what he's doing if he doesn't understand it, hey, he's likely learning this stuff for the first time, and while some people are fast learners, some people just take some time for the concepts to click. My HS calc teacher gave me some weird fuzzy explanation of why the integral is the backwards of a derivative and I had no clue what he was talking about, and he was all like " SEE? ISNT IT CLEAR?" so I was just like "w/e, I'll accept it." It wasn't until 3rd year that I understood his fuzzy explanation.
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EPT
