IrishBoy123
  • IrishBoy123
order of integration
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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IrishBoy123
  • IrishBoy123
show that \( \huge \int_{ 0}^{x} [ \int_{0}^{t} f(p) \ dp] \ dt = \int_{0}^{x} (x − p) \ f(p) \ dp\) by changing order of integration have a real blind spot on this, simply cannot visualise or draw it.
ganeshie8
  • ganeshie8
Hmm so \(x\) is a constant here.
ganeshie8
  • ganeshie8
lets sketch the curves representing the bounds |dw:1438709430741:dw|

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IrishBoy123
  • IrishBoy123
question
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IrishBoy123
  • IrishBoy123
solution
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ganeshie8
  • ganeshie8
that format files wont open on my system
Astrophysics
  • Astrophysics
|dw:1438709761438:dw| |dw:1438709783170:dw|
IrishBoy123
  • IrishBoy123
sorry i will try and convert it the RHS looks like a convolution from laplace, not that that helps me. the LHS has me seriously befuddled. i was thinking Fubini and double integrals, which i can usually handle, but no idea really
IrishBoy123
  • IrishBoy123
1 Attachment
ganeshie8
  • ganeshie8
|dw:1438709868443:dw|
IrishBoy123
  • IrishBoy123
1 Attachment
IrishBoy123
  • IrishBoy123
thank you @Astrophysics , very kind.
Astrophysics
  • Astrophysics
No problem :)
ganeshie8
  • ganeshie8
changing order of integration, do we get : \[\int\limits_{0}^x\int\limits_0^t f(p) dp\,dt~~=~~\int\limits_{0}^x\int\limits_p^x f(p) dt\,dp\]
Astrophysics
  • Astrophysics
Yes, that's what the solution shows
ganeshie8
  • ganeshie8
you may shoot an arrow and see the starting and leaving curves to setup the bounds : |dw:1438710530659:dw|
Astrophysics
  • Astrophysics
|dw:1438710651083:dw| When I used to do double integrals I did the same thing, it's easier to see