Does $int_{0}^{x} f(g_1(t),g_2(t)) dt - int_{0}^{x} f(g_1(t),g_2(x)) dt$ reduce in any meaningful way?
$begingroup$
I'm trying to figure out what $int_{0}^{x} f(g_1(t),g_2(t)) dt - int_{0}^{x} f(g_1(t),g_2(x)) dt$ reduces to, if anything. I know it does simplify to $int_{0}^{x} f(g_1(t),g_2(t)) - f(g_1(t),g_2(x)) dt$ but I curious as to whether any useful integration identities stem from this. I know that if $f(x,y) = x*y$ then it is the formula for integration by parts. I'm wondering if it extends to anything broader.
integration
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
$endgroup$
add a comment |
$begingroup$
I'm trying to figure out what $int_{0}^{x} f(g_1(t),g_2(t)) dt - int_{0}^{x} f(g_1(t),g_2(x)) dt$ reduces to, if anything. I know it does simplify to $int_{0}^{x} f(g_1(t),g_2(t)) - f(g_1(t),g_2(x)) dt$ but I curious as to whether any useful integration identities stem from this. I know that if $f(x,y) = x*y$ then it is the formula for integration by parts. I'm wondering if it extends to anything broader.
integration
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
$endgroup$
add a comment |
$begingroup$
I'm trying to figure out what $int_{0}^{x} f(g_1(t),g_2(t)) dt - int_{0}^{x} f(g_1(t),g_2(x)) dt$ reduces to, if anything. I know it does simplify to $int_{0}^{x} f(g_1(t),g_2(t)) - f(g_1(t),g_2(x)) dt$ but I curious as to whether any useful integration identities stem from this. I know that if $f(x,y) = x*y$ then it is the formula for integration by parts. I'm wondering if it extends to anything broader.
integration
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
$endgroup$
I'm trying to figure out what $int_{0}^{x} f(g_1(t),g_2(t)) dt - int_{0}^{x} f(g_1(t),g_2(x)) dt$ reduces to, if anything. I know it does simplify to $int_{0}^{x} f(g_1(t),g_2(t)) - f(g_1(t),g_2(x)) dt$ but I curious as to whether any useful integration identities stem from this. I know that if $f(x,y) = x*y$ then it is the formula for integration by parts. I'm wondering if it extends to anything broader.
integration
integration
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
asked Dec 4 '18 at 0:27
The Great DuckThe Great Duck
20632047
20632047
add a comment |
add a comment |
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