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Confusion in finding the definite integral
Clash Royale CLAN TAG#URR8PPP
up vote
5
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So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different.
Can someone please point out what I'm missing?
The answer from wolframAlpha is correct according to Casio fx-991-es
Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
calculus-and-analysis wolfram-alpha-queries
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
5
down vote
favorite
So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different.
Can someone please point out what I'm missing?
The answer from wolframAlpha is correct according to Casio fx-991-es
Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
calculus-and-analysis wolfram-alpha-queries
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.
– user6014
Sep 9 at 1:43
oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
– Ramith Hettiarachchi
Sep 9 at 1:45
add a comment |Â
up vote
5
down vote
favorite
up vote
5
down vote
favorite
So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different.
Can someone please point out what I'm missing?
The answer from wolframAlpha is correct according to Casio fx-991-es
Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
calculus-and-analysis wolfram-alpha-queries
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different.
Can someone please point out what I'm missing?
The answer from wolframAlpha is correct according to Casio fx-991-es
Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
calculus-and-analysis wolfram-alpha-queries
calculus-and-analysis wolfram-alpha-queries
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Sep 9 at 1:46
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
asked Sep 9 at 1:28
Ramith Hettiarachchi
283
283
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ramith Hettiarachchi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.
– user6014
Sep 9 at 1:43
oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
– Ramith Hettiarachchi
Sep 9 at 1:45
add a comment |Â
Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.
– user6014
Sep 9 at 1:43
oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
– Ramith Hettiarachchi
Sep 9 at 1:45
Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.
– user6014
Sep 9 at 1:43
Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.
– user6014
Sep 9 at 1:43
oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
– Ramith Hettiarachchi
Sep 9 at 1:45
oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
– Ramith Hettiarachchi
Sep 9 at 1:45
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
6
down vote
accepted
Precision issues. Use one of the following instead.
Symbolic integration:
Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, t, -4/5, 0]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)
N@%
(*0.00189205*)
Numeric integration with a higher working precision:
NIntegrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]
(*0.00189205*)
answered Sep 9 at 1:47
user6014
2,5721021
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
1
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of yourIntegrate[..], you get the same answer as theNIntegrate[..]in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such asIntegrateoften have trouble with "inexact" floating-point input. (3) Interesting aside:Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.
– Michael E2
2 days ago
 |Â
show 3 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
accepted
Precision issues. Use one of the following instead.
Symbolic integration:
Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, t, -4/5, 0]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)
N@%
(*0.00189205*)
Numeric integration with a higher working precision:
NIntegrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]
(*0.00189205*)
answered Sep 9 at 1:47
user6014
2,5721021
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
1
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of yourIntegrate[..], you get the same answer as theNIntegrate[..]in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such asIntegrateoften have trouble with "inexact" floating-point input. (3) Interesting aside:Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.
– Michael E2
2 days ago
 |Â
show 3 more comments
up vote
6
down vote
accepted
Precision issues. Use one of the following instead.
Symbolic integration:
Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, t, -4/5, 0]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)
N@%
(*0.00189205*)
Numeric integration with a higher working precision:
NIntegrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]
(*0.00189205*)
answered Sep 9 at 1:47
user6014
2,5721021
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
1
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of yourIntegrate[..], you get the same answer as theNIntegrate[..]in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such asIntegrateoften have trouble with "inexact" floating-point input. (3) Interesting aside:Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.
– Michael E2
2 days ago
 |Â
show 3 more comments
up vote
6
down vote
accepted
up vote
6
down vote
accepted
Precision issues. Use one of the following instead.
Symbolic integration:
Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, t, -4/5, 0]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)
N@%
(*0.00189205*)
Numeric integration with a higher working precision:
NIntegrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]
(*0.00189205*)
answered Sep 9 at 1:47
user6014
2,5721021
Precision issues. Use one of the following instead.
Symbolic integration:
Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, t, -4/5, 0]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)
N@%
(*0.00189205*)
Numeric integration with a higher working precision:
NIntegrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]
(*0.00189205*)
answered Sep 9 at 1:47
user6014
2,5721021
answered Sep 9 at 1:47
user6014
2,5721021
answered Sep 9 at 1:47
user6014
2,5721021
answered Sep 9 at 1:47
user6014
2,5721021
2,5721021
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
1
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of yourIntegrate[..], you get the same answer as theNIntegrate[..]in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such asIntegrateoften have trouble with "inexact" floating-point input. (3) Interesting aside:Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.
– Michael E2
2 days ago
 |Â
show 3 more comments
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
1
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of yourIntegrate[..], you get the same answer as theNIntegrate[..]in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such asIntegrateoften have trouble with "inexact" floating-point input. (3) Interesting aside:Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0]caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.
– Michael E2
2 days ago
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
Usually when do these issues occur? should i use NIntegrate instead?
– Ramith Hettiarachchi
Sep 9 at 1:52
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require.
– user6014
Sep 9 at 1:54
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results
– user6014
Sep 9 at 1:55
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
Appreciate your help 🙌Thanks!
– Ramith Hettiarachchi
Sep 9 at 1:57
1
1
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of your
Integrate[..], you get the same answer as the NIntegrate[..] in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such as Integrate often have trouble with "inexact" floating-point input. (3) Interesting aside: Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0] caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.– Michael E2
2 days ago
@RamithHettiarachchi -- (1) Note further that if you do just add an N in front of your
Integrate[..], you get the same answer as the NIntegrate[..] in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such as Integrate often have trouble with "inexact" floating-point input. (3) Interesting aside: Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, t, -.8`20, 0] caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems.– Michael E2
2 days ago
 |Â
show 3 more comments
Ramith Hettiarachchi is a new contributor. Be nice, and check out our Code of Conduct.
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Ramith Hettiarachchi is a new contributor. Be nice, and check out our Code of Conduct.
Ramith Hettiarachchi is a new contributor. Be nice, and check out our Code of Conduct.
Ramith Hettiarachchi is a new contributor. Be nice, and check out our Code of Conduct.
Â
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Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.
– user6014
Sep 9 at 1:43
oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, t, -0.8, 0]
– Ramith Hettiarachchi
Sep 9 at 1:45