upper and lower sum answer not matching
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I have to show that f is integrable using the Riemann criterion where
f(x) = x on [0, 1]. I am a bit confused over how my solution differs from the hint to solution of that question I have.
My approach is below:
Let partition P = {0 , 1/n , 2/n , ..... , (n-1)/n , n/n}.
So, U(P,f) = ∑(1/n) . { f(1/n) + f(2/n) + ....... + f(n/n) }
And, L(p,f) = ∑(1/n) . { f(0) + f(2/n) + ....... + f(n-1/n) }
Then, U(P,f) - L(P,f) = ( f(n/n) - f(0) )/n
= 1/n -> 0
Hint to solution given :
I am very confused over how did they get the result 1/n² , instead of my 1/n . Please help me out.
calculus
edited Nov 17 at 10:42
Parcly Taxel
41k137198
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
add a comment |
up vote
0
down vote
favorite
I have to show that f is integrable using the Riemann criterion where
f(x) = x on [0, 1]. I am a bit confused over how my solution differs from the hint to solution of that question I have.
My approach is below:
Let partition P = {0 , 1/n , 2/n , ..... , (n-1)/n , n/n}.
So, U(P,f) = ∑(1/n) . { f(1/n) + f(2/n) + ....... + f(n/n) }
And, L(p,f) = ∑(1/n) . { f(0) + f(2/n) + ....... + f(n-1/n) }
Then, U(P,f) - L(P,f) = ( f(n/n) - f(0) )/n
= 1/n -> 0
Hint to solution given :
I am very confused over how did they get the result 1/n² , instead of my 1/n . Please help me out.
calculus
edited Nov 17 at 10:42
Parcly Taxel
41k137198
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
1
I believe the hint is wrong.
– B. Goddard
Nov 17 at 13:42
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have to show that f is integrable using the Riemann criterion where
f(x) = x on [0, 1]. I am a bit confused over how my solution differs from the hint to solution of that question I have.
My approach is below:
Let partition P = {0 , 1/n , 2/n , ..... , (n-1)/n , n/n}.
So, U(P,f) = ∑(1/n) . { f(1/n) + f(2/n) + ....... + f(n/n) }
And, L(p,f) = ∑(1/n) . { f(0) + f(2/n) + ....... + f(n-1/n) }
Then, U(P,f) - L(P,f) = ( f(n/n) - f(0) )/n
= 1/n -> 0
Hint to solution given :
I am very confused over how did they get the result 1/n² , instead of my 1/n . Please help me out.
calculus
edited Nov 17 at 10:42
Parcly Taxel
41k137198
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
I have to show that f is integrable using the Riemann criterion where
f(x) = x on [0, 1]. I am a bit confused over how my solution differs from the hint to solution of that question I have.
My approach is below:
Let partition P = {0 , 1/n , 2/n , ..... , (n-1)/n , n/n}.
So, U(P,f) = ∑(1/n) . { f(1/n) + f(2/n) + ....... + f(n/n) }
And, L(p,f) = ∑(1/n) . { f(0) + f(2/n) + ....... + f(n-1/n) }
Then, U(P,f) - L(P,f) = ( f(n/n) - f(0) )/n
= 1/n -> 0
Hint to solution given :
I am very confused over how did they get the result 1/n² , instead of my 1/n . Please help me out.
calculus
calculus
edited Nov 17 at 10:42
Parcly Taxel
41k137198
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
edited Nov 17 at 10:42
Parcly Taxel
41k137198
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
edited Nov 17 at 10:42
Parcly Taxel
41k137198
edited Nov 17 at 10:42
Parcly Taxel
41k137198
edited Nov 17 at 10:42
Parcly Taxel
41k137198
41k137198
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
asked Nov 17 at 10:42
Kaustav Bhattacharjee
61
61
1
I believe the hint is wrong.
– B. Goddard
Nov 17 at 13:42
add a comment |
1
I believe the hint is wrong.
– B. Goddard
Nov 17 at 13:42
1
1
I believe the hint is wrong.
– B. Goddard
Nov 17 at 13:42
I believe the hint is wrong.
– B. Goddard
Nov 17 at 13:42
add a comment |
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I believe the hint is wrong.
– B. Goddard
Nov 17 at 13:42