Integral $int_{[1,2]times[0,pi]}log(sqrt{x})sin(2y)d(x,y)$
I want to find out if this integral can be calculated (if it exists)
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y)$$
To be honest, I don't know how, but I think that one might has to use Fubini's theorem since this is an iterated integral. Does someone know how it's done? And can someone explain to me what is meant with the interval $[1,2]times[0,pi]$?
I did this, but I don't know how to continue.
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y) = dfrac{sinleft(2yright)lnleft(xright)}{2} = frac{sin(2y)}{2} int{ln(x)}~dx$$
Here's what the function looks like, it looks nice imo.
integration analysis functions iterated-integrals
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
add a comment |
I want to find out if this integral can be calculated (if it exists)
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y)$$
To be honest, I don't know how, but I think that one might has to use Fubini's theorem since this is an iterated integral. Does someone know how it's done? And can someone explain to me what is meant with the interval $[1,2]times[0,pi]$?
I did this, but I don't know how to continue.
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y) = dfrac{sinleft(2yright)lnleft(xright)}{2} = frac{sin(2y)}{2} int{ln(x)}~dx$$
Here's what the function looks like, it looks nice imo.
integration analysis functions iterated-integrals
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
What does $d(x,y)$ mean? Do you mean $dxdy$?
– Mostafa Ayaz
Dec 3 '18 at 22:18
1
The integral is obviously zero.
– Did
Dec 3 '18 at 23:30
add a comment |
I want to find out if this integral can be calculated (if it exists)
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y)$$
To be honest, I don't know how, but I think that one might has to use Fubini's theorem since this is an iterated integral. Does someone know how it's done? And can someone explain to me what is meant with the interval $[1,2]times[0,pi]$?
I did this, but I don't know how to continue.
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y) = dfrac{sinleft(2yright)lnleft(xright)}{2} = frac{sin(2y)}{2} int{ln(x)}~dx$$
Here's what the function looks like, it looks nice imo.
integration analysis functions iterated-integrals
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
I want to find out if this integral can be calculated (if it exists)
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y)$$
To be honest, I don't know how, but I think that one might has to use Fubini's theorem since this is an iterated integral. Does someone know how it's done? And can someone explain to me what is meant with the interval $[1,2]times[0,pi]$?
I did this, but I don't know how to continue.
$$int_{[1,2]times[0,pi]} log(sqrt{x})sin(2y)~d(x,y) = dfrac{sinleft(2yright)lnleft(xright)}{2} = frac{sin(2y)}{2} int{ln(x)}~dx$$
Here's what the function looks like, it looks nice imo.
integration analysis functions iterated-integrals
integration analysis functions iterated-integrals
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
edited Dec 4 '18 at 10:13
Asaf Karagila♦
302k32426756
302k32426756
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
asked Dec 3 '18 at 22:15
Ramanujan Taylor
184
184
What does $d(x,y)$ mean? Do you mean $dxdy$?
– Mostafa Ayaz
Dec 3 '18 at 22:18
1
The integral is obviously zero.
– Did
Dec 3 '18 at 23:30
add a comment |
What does $d(x,y)$ mean? Do you mean $dxdy$?
– Mostafa Ayaz
Dec 3 '18 at 22:18
1
The integral is obviously zero.
– Did
Dec 3 '18 at 23:30
What does $d(x,y)$ mean? Do you mean $dxdy$?
– Mostafa Ayaz
Dec 3 '18 at 22:18
What does $d(x,y)$ mean? Do you mean $dxdy$?
– Mostafa Ayaz
Dec 3 '18 at 22:18
1
1
The integral is obviously zero.
– Did
Dec 3 '18 at 23:30
The integral is obviously zero.
– Did
Dec 3 '18 at 23:30
add a comment |
1 Answer
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Hint: the integral means $int_1^2 int_0^{pi}$. Further,
$$int_1^2int_0^pi f(x)g(y),dy,dx = left(int_1^2 f(x),dxright)left(int_0^pi g(y),dyright).$$
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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oldest
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active
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Hint: the integral means $int_1^2 int_0^{pi}$. Further,
$$int_1^2int_0^pi f(x)g(y),dy,dx = left(int_1^2 f(x),dxright)left(int_0^pi g(y),dyright).$$
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
add a comment |
Hint: the integral means $int_1^2 int_0^{pi}$. Further,
$$int_1^2int_0^pi f(x)g(y),dy,dx = left(int_1^2 f(x),dxright)left(int_0^pi g(y),dyright).$$
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
add a comment |
Hint: the integral means $int_1^2 int_0^{pi}$. Further,
$$int_1^2int_0^pi f(x)g(y),dy,dx = left(int_1^2 f(x),dxright)left(int_0^pi g(y),dyright).$$
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
Hint: the integral means $int_1^2 int_0^{pi}$. Further,
$$int_1^2int_0^pi f(x)g(y),dy,dx = left(int_1^2 f(x),dxright)left(int_0^pi g(y),dyright).$$
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
answered Dec 3 '18 at 23:27
rogerl
17.4k22746
17.4k22746
add a comment |
add a comment |
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What does $d(x,y)$ mean? Do you mean $dxdy$?
– Mostafa Ayaz
Dec 3 '18 at 22:18
1
The integral is obviously zero.
– Did
Dec 3 '18 at 23:30