Mixing
change of variables in integral - how do limits change?
$begingroup$
If I have this integral:
$$int_0^{sigma_0}xR^2dR$$
and I know that $x=frac{R}
{sigma_0}$
and I substitute:
$$int x (xsigma_0)^2 dx= int x^3 sigma_0^2 dx$$
what are the new integration limits?
integration change-of-variable
edited Feb 2 at 3:17
timtfj
2,523420
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
$endgroup$
add a comment |
$begingroup$
If I have this integral:
$$int_0^{sigma_0}xR^2dR$$
and I know that $x=frac{R}
{sigma_0}$
and I substitute:
$$int x (xsigma_0)^2 dx= int x^3 sigma_0^2 dx$$
what are the new integration limits?
integration change-of-variable
edited Feb 2 at 3:17
timtfj
2,523420
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
$endgroup$
$begingroup$
To put formulas into display format (= on their own line, big integral signs etc.) simply use double dollar signs round them. (That's all I did in my edit, other than editing the fraction.)
$endgroup$
– timtfj
Feb 2 at 3:24
add a comment |
$begingroup$
If I have this integral:
$$int_0^{sigma_0}xR^2dR$$
and I know that $x=frac{R}
{sigma_0}$
and I substitute:
$$int x (xsigma_0)^2 dx= int x^3 sigma_0^2 dx$$
what are the new integration limits?
integration change-of-variable
edited Feb 2 at 3:17
timtfj
2,523420
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
$endgroup$
If I have this integral:
$$int_0^{sigma_0}xR^2dR$$
and I know that $x=frac{R}
{sigma_0}$
and I substitute:
$$int x (xsigma_0)^2 dx= int x^3 sigma_0^2 dx$$
what are the new integration limits?
integration change-of-variable
integration change-of-variable
edited Feb 2 at 3:17
timtfj
2,523420
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
edited Feb 2 at 3:17
timtfj
2,523420
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
edited Feb 2 at 3:17
timtfj
2,523420
edited Feb 2 at 3:17
timtfj
2,523420
edited Feb 2 at 3:17
timtfj
2,523420
2,523420
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
asked Feb 1 at 22:56
Jackson HartJackson Hart
5402726
5402726
$begingroup$
To put formulas into display format (= on their own line, big integral signs etc.) simply use double dollar signs round them. (That's all I did in my edit, other than editing the fraction.)
$endgroup$
– timtfj
Feb 2 at 3:24
add a comment |
$begingroup$
To put formulas into display format (= on their own line, big integral signs etc.) simply use double dollar signs round them. (That's all I did in my edit, other than editing the fraction.)
$endgroup$
– timtfj
Feb 2 at 3:24
$begingroup$
To put formulas into display format (= on their own line, big integral signs etc.) simply use double dollar signs round them. (That's all I did in my edit, other than editing the fraction.)
$endgroup$
– timtfj
Feb 2 at 3:24
$begingroup$
To put formulas into display format (= on their own line, big integral signs etc.) simply use double dollar signs round them. (That's all I did in my edit, other than editing the fraction.)
$endgroup$
– timtfj
Feb 2 at 3:24
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The limits of integration are given as $R= 0$ and $R= sigma_0$. You change variables from R to $x= frac{R}{sigma_0}$. When $R= 0$, then, $x= frac{0}{sigma_0}= 0$. When $R= sigma_0$, $x= frac{sigma_0}{sigma_0}= 1$
answered Feb 1 at 23:08
user247327user247327
11.6k1516
$endgroup$
add a comment |
$begingroup$
Simply replace the integration limits according to the substitution. The new extremes turn out to be $0$ and $1$.
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
$endgroup$
add a comment |
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2 Answers
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active
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2 Answers
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active
oldest
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$begingroup$
The limits of integration are given as $R= 0$ and $R= sigma_0$. You change variables from R to $x= frac{R}{sigma_0}$. When $R= 0$, then, $x= frac{0}{sigma_0}= 0$. When $R= sigma_0$, $x= frac{sigma_0}{sigma_0}= 1$
answered Feb 1 at 23:08
user247327user247327
11.6k1516
$endgroup$
add a comment |
$begingroup$
The limits of integration are given as $R= 0$ and $R= sigma_0$. You change variables from R to $x= frac{R}{sigma_0}$. When $R= 0$, then, $x= frac{0}{sigma_0}= 0$. When $R= sigma_0$, $x= frac{sigma_0}{sigma_0}= 1$
answered Feb 1 at 23:08
user247327user247327
11.6k1516
$endgroup$
add a comment |
$begingroup$
The limits of integration are given as $R= 0$ and $R= sigma_0$. You change variables from R to $x= frac{R}{sigma_0}$. When $R= 0$, then, $x= frac{0}{sigma_0}= 0$. When $R= sigma_0$, $x= frac{sigma_0}{sigma_0}= 1$
answered Feb 1 at 23:08
user247327user247327
11.6k1516
$endgroup$
The limits of integration are given as $R= 0$ and $R= sigma_0$. You change variables from R to $x= frac{R}{sigma_0}$. When $R= 0$, then, $x= frac{0}{sigma_0}= 0$. When $R= sigma_0$, $x= frac{sigma_0}{sigma_0}= 1$
answered Feb 1 at 23:08
user247327user247327
11.6k1516
answered Feb 1 at 23:08
user247327user247327
11.6k1516
answered Feb 1 at 23:08
user247327user247327
11.6k1516
answered Feb 1 at 23:08
user247327user247327
11.6k1516
11.6k1516
add a comment |
add a comment |
$begingroup$
Simply replace the integration limits according to the substitution. The new extremes turn out to be $0$ and $1$.
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
$endgroup$
add a comment |
$begingroup$
Simply replace the integration limits according to the substitution. The new extremes turn out to be $0$ and $1$.
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
$endgroup$
add a comment |
$begingroup$
Simply replace the integration limits according to the substitution. The new extremes turn out to be $0$ and $1$.
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
$endgroup$
Simply replace the integration limits according to the substitution. The new extremes turn out to be $0$ and $1$.
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
answered Feb 1 at 23:00
AlessioDVAlessioDV
1,208114
1,208114
add a comment |
add a comment |
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$begingroup$
To put formulas into display format (= on their own line, big integral signs etc.) simply use double dollar signs round them. (That's all I did in my edit, other than editing the fraction.)
$endgroup$
– timtfj
Feb 2 at 3:24