Definite integral's basic question on definition
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Limits with definite integration
Please see this link and then answer my query.
My question:
Why can't we integrate with the variable like that is given? What is the reason for it? Please explain in simple terms... (A beginner :-))
(Reason for both the question as well as for the attempt)
definite-integrals definition
asked Sep 10 at 18:57
jayant98
709
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up vote
0
down vote
favorite
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Limits with definite integration
Please see this link and then answer my query.
My question:
Why can't we integrate with the variable like that is given? What is the reason for it? Please explain in simple terms... (A beginner :-))
(Reason for both the question as well as for the attempt)
definite-integrals definition
asked Sep 10 at 18:57
jayant98
709
1
The siplest explanation is to avoid confusion. The limits on the definite integral are specific values of the argument, while the variable of integration is a dummy, where any letter can be used. For example $int_a^bf(x)dx=int_a^bf(y)dy$. If you want $b$ to be $x$, the first form might be confusing, while the second is clear. This avoids problems when the integral with $x$ as a limit appears inside another expression, where x plays a role.
– herb steinberg
Sep 10 at 19:04
Okay. I got the x in the $f(x) $ is just a dummy variable. but why the first form creates confusion? I mean it may be treated as the second form. Just simple. Or is it just the convention to be like that only? Because what we use in the Newton Leibnitz type problems it has some time limits of function such as 0 to $x$ and the integarting function is f(x, t).
– jayant98
Sep 10 at 19:12
Please feel free to tell me if I am mixing up these two concepts. And about the remedies also. :-)
– jayant98
Sep 10 at 19:14
My feeling is that you are overthinking the situation. As long as you can clearly make the distinction between the upper limit argument and the dummy, you won't have any problem. I have seen confusion when iterated integrals or multiple integrals are used and the limits involve the arguments. In these cases it is absolutely necessary to use different letters for the dummy.
– herb steinberg
Sep 10 at 19:25
Oh. Okay. I think you are right : I am just overthinking. Well, thanks again for helping me. :-)
– jayant98
Sep 10 at 19:27
add a comment |Â
up vote
0
down vote
favorite
1
up vote
0
down vote
favorite
1
1
Limits with definite integration
Please see this link and then answer my query.
My question:
Why can't we integrate with the variable like that is given? What is the reason for it? Please explain in simple terms... (A beginner :-))
(Reason for both the question as well as for the attempt)
definite-integrals definition
asked Sep 10 at 18:57
jayant98
709
Limits with definite integration
Please see this link and then answer my query.
My question:
Why can't we integrate with the variable like that is given? What is the reason for it? Please explain in simple terms... (A beginner :-))
(Reason for both the question as well as for the attempt)
definite-integrals definition
definite-integrals definition
asked Sep 10 at 18:57
jayant98
709
asked Sep 10 at 18:57
jayant98
709
asked Sep 10 at 18:57
jayant98
709
asked Sep 10 at 18:57
jayant98
709
asked Sep 10 at 18:57
jayant98
709
709
1
The siplest explanation is to avoid confusion. The limits on the definite integral are specific values of the argument, while the variable of integration is a dummy, where any letter can be used. For example $int_a^bf(x)dx=int_a^bf(y)dy$. If you want $b$ to be $x$, the first form might be confusing, while the second is clear. This avoids problems when the integral with $x$ as a limit appears inside another expression, where x plays a role.
– herb steinberg
Sep 10 at 19:04
Okay. I got the x in the $f(x) $ is just a dummy variable. but why the first form creates confusion? I mean it may be treated as the second form. Just simple. Or is it just the convention to be like that only? Because what we use in the Newton Leibnitz type problems it has some time limits of function such as 0 to $x$ and the integarting function is f(x, t).
– jayant98
Sep 10 at 19:12
Please feel free to tell me if I am mixing up these two concepts. And about the remedies also. :-)
– jayant98
Sep 10 at 19:14
My feeling is that you are overthinking the situation. As long as you can clearly make the distinction between the upper limit argument and the dummy, you won't have any problem. I have seen confusion when iterated integrals or multiple integrals are used and the limits involve the arguments. In these cases it is absolutely necessary to use different letters for the dummy.
– herb steinberg
Sep 10 at 19:25
Oh. Okay. I think you are right : I am just overthinking. Well, thanks again for helping me. :-)
– jayant98
Sep 10 at 19:27
add a comment |Â
1
The siplest explanation is to avoid confusion. The limits on the definite integral are specific values of the argument, while the variable of integration is a dummy, where any letter can be used. For example $int_a^bf(x)dx=int_a^bf(y)dy$. If you want $b$ to be $x$, the first form might be confusing, while the second is clear. This avoids problems when the integral with $x$ as a limit appears inside another expression, where x plays a role.
– herb steinberg
Sep 10 at 19:04
Okay. I got the x in the $f(x) $ is just a dummy variable. but why the first form creates confusion? I mean it may be treated as the second form. Just simple. Or is it just the convention to be like that only? Because what we use in the Newton Leibnitz type problems it has some time limits of function such as 0 to $x$ and the integarting function is f(x, t).
– jayant98
Sep 10 at 19:12
Please feel free to tell me if I am mixing up these two concepts. And about the remedies also. :-)
– jayant98
Sep 10 at 19:14
My feeling is that you are overthinking the situation. As long as you can clearly make the distinction between the upper limit argument and the dummy, you won't have any problem. I have seen confusion when iterated integrals or multiple integrals are used and the limits involve the arguments. In these cases it is absolutely necessary to use different letters for the dummy.
– herb steinberg
Sep 10 at 19:25
Oh. Okay. I think you are right : I am just overthinking. Well, thanks again for helping me. :-)
– jayant98
Sep 10 at 19:27
1
1
The siplest explanation is to avoid confusion. The limits on the definite integral are specific values of the argument, while the variable of integration is a dummy, where any letter can be used. For example $int_a^bf(x)dx=int_a^bf(y)dy$. If you want $b$ to be $x$, the first form might be confusing, while the second is clear. This avoids problems when the integral with $x$ as a limit appears inside another expression, where x plays a role.
– herb steinberg
Sep 10 at 19:04
The siplest explanation is to avoid confusion. The limits on the definite integral are specific values of the argument, while the variable of integration is a dummy, where any letter can be used. For example $int_a^bf(x)dx=int_a^bf(y)dy$. If you want $b$ to be $x$, the first form might be confusing, while the second is clear. This avoids problems when the integral with $x$ as a limit appears inside another expression, where x plays a role.
– herb steinberg
Sep 10 at 19:04
Okay. I got the x in the $f(x) $ is just a dummy variable. but why the first form creates confusion? I mean it may be treated as the second form. Just simple. Or is it just the convention to be like that only? Because what we use in the Newton Leibnitz type problems it has some time limits of function such as 0 to $x$ and the integarting function is f(x, t).
– jayant98
Sep 10 at 19:12
Okay. I got the x in the $f(x) $ is just a dummy variable. but why the first form creates confusion? I mean it may be treated as the second form. Just simple. Or is it just the convention to be like that only? Because what we use in the Newton Leibnitz type problems it has some time limits of function such as 0 to $x$ and the integarting function is f(x, t).
– jayant98
Sep 10 at 19:12
Please feel free to tell me if I am mixing up these two concepts. And about the remedies also. :-)
– jayant98
Sep 10 at 19:14
Please feel free to tell me if I am mixing up these two concepts. And about the remedies also. :-)
– jayant98
Sep 10 at 19:14
My feeling is that you are overthinking the situation. As long as you can clearly make the distinction between the upper limit argument and the dummy, you won't have any problem. I have seen confusion when iterated integrals or multiple integrals are used and the limits involve the arguments. In these cases it is absolutely necessary to use different letters for the dummy.
– herb steinberg
Sep 10 at 19:25
My feeling is that you are overthinking the situation. As long as you can clearly make the distinction between the upper limit argument and the dummy, you won't have any problem. I have seen confusion when iterated integrals or multiple integrals are used and the limits involve the arguments. In these cases it is absolutely necessary to use different letters for the dummy.
– herb steinberg
Sep 10 at 19:25
Oh. Okay. I think you are right : I am just overthinking. Well, thanks again for helping me. :-)
– jayant98
Sep 10 at 19:27
Oh. Okay. I think you are right : I am just overthinking. Well, thanks again for helping me. :-)
– jayant98
Sep 10 at 19:27
add a comment |Â
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The siplest explanation is to avoid confusion. The limits on the definite integral are specific values of the argument, while the variable of integration is a dummy, where any letter can be used. For example $int_a^bf(x)dx=int_a^bf(y)dy$. If you want $b$ to be $x$, the first form might be confusing, while the second is clear. This avoids problems when the integral with $x$ as a limit appears inside another expression, where x plays a role.
– herb steinberg
Sep 10 at 19:04
Okay. I got the x in the $f(x) $ is just a dummy variable. but why the first form creates confusion? I mean it may be treated as the second form. Just simple. Or is it just the convention to be like that only? Because what we use in the Newton Leibnitz type problems it has some time limits of function such as 0 to $x$ and the integarting function is f(x, t).
– jayant98
Sep 10 at 19:12
Please feel free to tell me if I am mixing up these two concepts. And about the remedies also. :-)
– jayant98
Sep 10 at 19:14
My feeling is that you are overthinking the situation. As long as you can clearly make the distinction between the upper limit argument and the dummy, you won't have any problem. I have seen confusion when iterated integrals or multiple integrals are used and the limits involve the arguments. In these cases it is absolutely necessary to use different letters for the dummy.
– herb steinberg
Sep 10 at 19:25
Oh. Okay. I think you are right : I am just overthinking. Well, thanks again for helping me. :-)
– jayant98
Sep 10 at 19:27