Recent content by irresistible

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    Riemann Integral - little proof help

    Homework Statement Suppose f is integrable for all x in[a,b] and f(x)>C ( C is some constant), Must show that 1/f is also integrable. Homework Equations f is integrable implies Upf-Lpf<\epsilon for some partition in [a,b] The Attempt at a Solution Therefore, I must come up...
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    Java Need help setting up arrays for Galton box simulation?

    I'm new in java and I'm trying to come up with a program that stimulates the bean machine(also known as Galton box) Balls are dropped from the opening of the board. Everytime a ball hits, there is a 50% chance to fall to left and 50% chance to fall to the right. the piles of balls are...
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    R twice continuously differentiable function proof

    the inequality makes sense now that you explained, I still have trouble proving it, Where do I use the fact that f is TWICE differentiable?Does that make a difference?
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    Show that F'(x) exists for all x [tex]\in[a,b] [/tex]

    F'(x) will be Undefined as x approaches zero \rightarrow unbounded \rightarrow non integrable ?
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    R twice continuously differentiable function proof

    r twice continuously differentiable function proof... Homework Statement Help :frown: if f:[a,b] \rightarrow R is twice continuously differentiable, and f(x)\geq 0 for all x in [a.b] and f ''(x) \leq 0 for all x in [a,b] prove that 1/2 (f(a) + f(b)) (b-a) \leq \int f(x)dx \leq(b-a)...
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    Show that F'(x) exists for all x [tex]\in[a,b] [/tex]

    right, But I think you made a little mistake with differentiation, I think it will be: F'(x)= 2x sin(1/x2) - 2cos(1/x2)/ x Which still, limits exists. But How do I prove that F'(x) is unbounded?
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    Graduate Examples of Pointwise Convergence of Integrable Functions to Non-Integrable

    hey guys, Any one can think of any examples ? Of a sequence of integrable functions{fn} on [0,1] that converges pointwise to a non-integrable function f:[0,1] --> R ??
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    Show that F'(x) exists for all x [tex]\in[a,b] [/tex]

    Homework Statement Consider F(x) = x2 sin(1/x2) if 0<x\leq1 and = 0 if x\leq0 Show that F'(x) exists for all x \in[a,b] but that F':[0,1] \rightarrow1 is not integrable. Homework Equations So we have to show we do not have F(1)-F(0) = \int F'(x)dx (integral...
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    If f:[0,1] -> R is a continuous function, describe f.

    I think so,Thank you
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    If f:[0,1] -> R is a continuous function, describe f.

    Homework Statement f:[0,1] \rightarrow R is a continuous function such that \intf(t)dt (from 0 to x) = \int f(t)dt( from x to 1) for all x\in[0,1] . Describe f. Homework Equations integral represents area The Attempt at a Solution what ever the function is, I know that...
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    Graduate Proving F'(x)= f(x) using the definition of integral?

    Hey guys, Can you help me prove this? Suppose that f:[a.b] -> R is integrable and that F:[a,b]->R is a differentiable function such thet F'(x)= f(x) for all xLaTeX Code: \\in [a,b]. Prove from the definition of the integral that; F(b)-F(a) =LaTeX Code: \\int f(x) dx ( integral going from...
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    Undergrad Proving F'(x)= f(x) using the definition of integral?

    sorry, I'm new here I'm going to post it over there and delete this one if possible
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    Undergrad Proving F'(x)= f(x) using the definition of integral?

    Hey guys,:smile: Can you help me prove this?:confused: Suppose that f:[a.b] -> R is integrable and that F:[a,b]->R is a differentiable function such thet F'(x)= f(x) for all x\in [a,b]. Prove from the definition of the integral that; F(b)-F(a) =\int f(x) dx ( integral going from a to b)...
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    Graduate Example of a non-integrable function f , such that |f| and f^2 are integrable?

    Oh I don't know why I didn't think of that! Thank you so much to both of youuuu! :smile:
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    Graduate Example of a non-integrable function f , such that |f| and f^2 are integrable?

    I'm looking for a function f:[a,b] -> R such that |f| and f2 are integrable on [a,b] any helps?