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?
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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 at 0:27
The Great Duck
10632047
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up vote
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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 at 0:27
The Great Duck
10632047
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 at 0:27
The Great Duck
10632047
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 at 0:27
The Great Duck
10632047
asked Dec 4 at 0:27
The Great Duck
10632047
asked Dec 4 at 0:27
The Great Duck
10632047
asked Dec 4 at 0:27
The Great Duck
10632047
asked Dec 4 at 0:27
The Great Duck
10632047
10632047
add a comment |
add a comment |
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