Proof of an integral property [on hold]
$begingroup$
$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$
calculus integration definite-integrals
edited yesterday
Eevee Trainer
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adam hanyadam hany
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put on hold as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen 5 hours ago
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add a comment |
$begingroup$
$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$
calculus integration definite-integrals
edited yesterday
Eevee Trainer
6,56811237
asked yesterday
adam hanyadam hany
211
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.
8
$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
yesterday
add a comment |
$begingroup$
$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$
calculus integration definite-integrals
edited yesterday
Eevee Trainer
6,56811237
asked yesterday
adam hanyadam hany
211
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$
calculus integration definite-integrals
calculus integration definite-integrals
edited yesterday
Eevee Trainer
6,56811237
asked yesterday
adam hanyadam hany
211
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Eevee Trainer
6,56811237
asked yesterday
adam hanyadam hany
211
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Eevee Trainer
6,56811237
edited yesterday
Eevee Trainer
6,56811237
edited yesterday
Eevee Trainer
6,56811237
6,56811237
asked yesterday
adam hanyadam hany
211
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
adam hanyadam hany
211
asked yesterday
adam hanyadam hany
211
211
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
adam hany is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.
8
$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
yesterday
add a comment |
8
$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
yesterday
8
8
$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
yesterday
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Hint:
Utilize integration by parts:
$$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$
If we have a definite integral, then this formula becomes
$$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$
edited yesterday
mrtaurho
5,51551439
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
1
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
add a comment |
$begingroup$
Hint:
$$dfrac{d(f(x)cdot g(x))}{dx}=?$$
Integrate both sides with respect to $x$ between $[0,1]$
edited yesterday
Eevee Trainer
6,56811237
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:
Utilize integration by parts:
$$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$
If we have a definite integral, then this formula becomes
$$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$
edited yesterday
mrtaurho
5,51551439
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
1
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
add a comment |
$begingroup$
Hint:
Utilize integration by parts:
$$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$
If we have a definite integral, then this formula becomes
$$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$
edited yesterday
mrtaurho
5,51551439
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
1
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
add a comment |
$begingroup$
Hint:
Utilize integration by parts:
$$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$
If we have a definite integral, then this formula becomes
$$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$
edited yesterday
mrtaurho
5,51551439
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
Hint:
Utilize integration by parts:
$$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$
If we have a definite integral, then this formula becomes
$$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$
edited yesterday
mrtaurho
5,51551439
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
edited yesterday
mrtaurho
5,51551439
edited yesterday
mrtaurho
5,51551439
edited yesterday
mrtaurho
5,51551439
5,51551439
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
answered yesterday
Eevee TrainerEevee Trainer
6,56811237
6,56811237
1
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
add a comment |
1
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
1
1
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
$begingroup$
thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
$endgroup$
– adam hany
yesterday
add a comment |
$begingroup$
Hint:
$$dfrac{d(f(x)cdot g(x))}{dx}=?$$
Integrate both sides with respect to $x$ between $[0,1]$
edited yesterday
Eevee Trainer
6,56811237
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
add a comment |
$begingroup$
Hint:
$$dfrac{d(f(x)cdot g(x))}{dx}=?$$
Integrate both sides with respect to $x$ between $[0,1]$
edited yesterday
Eevee Trainer
6,56811237
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
add a comment |
$begingroup$
Hint:
$$dfrac{d(f(x)cdot g(x))}{dx}=?$$
Integrate both sides with respect to $x$ between $[0,1]$
edited yesterday
Eevee Trainer
6,56811237
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
Hint:
$$dfrac{d(f(x)cdot g(x))}{dx}=?$$
Integrate both sides with respect to $x$ between $[0,1]$
edited yesterday
Eevee Trainer
6,56811237
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
edited yesterday
Eevee Trainer
6,56811237
edited yesterday
Eevee Trainer
6,56811237
edited yesterday
Eevee Trainer
6,56811237
6,56811237
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
answered yesterday
lab bhattacharjeelab bhattacharjee
226k15157275
226k15157275
add a comment |
add a comment |
8
$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
yesterday