Question

if f and g are riemann integrable on [a b] , g is non negative and f is bounded

score 158 · Answer 1 · 2017-02-12 18:04:25

158

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if f and g are riemann integrable on [a b] , g is non negative and f is bounded

Published on 12 Feb 2017 - 18:04

score 1.5k · Answer 2 · 2017-02-16 02:14:14

1.5k

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Prove the Cauchy Criterion for Riemann-Stieltjes Integrability

Published on 16 Feb 2017 - 2:14

score 91 · Answer 3 · 2017-02-16 14:54:16

91

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integrable riemann function

Published on 16 Feb 2017 - 14:54

score 61 · Answer 4 · 2017-02-17 05:15:35

61

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Show that $A\int_If=\int_I Af$ for some bounded linear operator $A$

Published on 17 Feb 2017 - 5:15

score 49 · Answer 5 · 2017-02-17 06:56:55

49

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What conditions on $f$ ensure that $\forall c<a<b<d$, $\frac{1}{b-a}\int_{a}^{b}f(x) dx \leq \int_{c}^{d}f(x)dx$?

Published on 17 Feb 2017 - 6:56

score 762 · Answer 6 · 2017-02-17 13:47:51

762

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Limit of the Riemann sum $ \sum_{i=1}^n \sin({i\pi \over n}){\pi \over n}$

Published on 17 Feb 2017 - 13:47

score 1.2k · Answer 7 · 2017-02-19 18:00:23

1.2k

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Can you use the substitution $t=\tan(x/2)$ to solve $\int \frac{1}{\cos x}dx$?

Published on 19 Feb 2017 - 18:00

score 2.6k · Answer 8 · 2017-02-19 19:13:42

2.6k

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Comparing Lebesgue integral and Riemann Stieltjes integral

Published on 19 Feb 2017 - 19:13

score 94 · Answer 9 · 2017-02-21 20:19:07

94

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Riemann-integrability of function with countably many discontinuities

Published on 21 Feb 2017 - 20:19

score 1.2k · Answer 10 · 2017-02-22 05:48:15

1.2k

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Let $f\in\mathfrak R[0,1],\tau_n=\{0,\frac1n,\ldots,\frac nn\}$, & $\lim_{n\to\infty}U[f;\tau_n]=\lim_{n\to\infty}L[f;\tau_n]=A$. Prove $\int_0^1f=A$

Published on 22 Feb 2017 - 5:48

score 81 · Answer 11 · 2017-02-22 18:36:11

81

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Why is this Riemann integral $0$?

Published on 22 Feb 2017 - 18:36

score 1.3k · Answer 12 · 2017-02-23 16:59:40

1.3k

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Proof that if $f$ is Continuous on $[a,b]$, it is Riemann Integrable on $[a,b]$.

Published on 23 Feb 2017 - 16:59

score 36 · Answer 13 · 2017-02-24 10:39:52

36

Views

2 integrable functions

Published on 24 Feb 2017 - 10:39

score 59 · Answer 14 · 2017-02-24 11:23:35

59

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fundamental theorem of calculus

Published on 24 Feb 2017 - 11:23

score 112 · Answer 15 · 2017-02-25 08:29:59

112

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Taking out limit from integral of limit.

Published on 25 Feb 2017 - 8:29

List Question

if f and g are riemann integrable on [a b] , g is non negative and f is bounded

Prove the Cauchy Criterion for Riemann-Stieltjes Integrability

integrable riemann function

Show that $A\int_If=\int_I Af$ for some bounded linear operator $A$

What conditions on $f$ ensure that $\forall c<a<b<d$, $\frac{1}{b-a}\int_{a}^{b}f(x) dx \leq \int_{c}^{d}f(x)dx$?

Limit of the Riemann sum $ \sum_{i=1}^n \sin({i\pi \over n}){\pi \over n}$

Can you use the substitution $t=\tan(x/2)$ to solve $\int \frac{1}{\cos x}dx$?

Comparing Lebesgue integral and Riemann Stieltjes integral

Riemann-integrability of function with countably many discontinuities

Let $f\in\mathfrak R[0,1],\tau_n=\{0,\frac1n,\ldots,\frac nn\}$, & $\lim_{n\to\infty}U[f;\tau_n]=\lim_{n\to\infty}L[f;\tau_n]=A$. Prove $\int_0^1f=A$

Why is this Riemann integral $0$?

Proof that if $f$ is Continuous on $[a,b]$, it is Riemann Integrable on $[a,b]$.

2 integrable functions

fundamental theorem of calculus

Taking out limit from integral of limit.

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