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IrishBoy123
 one year ago
order of integration
IrishBoy123
 one year ago
order of integration

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1show 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
 one year ago
Best ResponseYou've already chosen the best response.4Hmm so \(x\) is a constant here.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4lets sketch the curves representing the bounds dw:1438709430741:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4that format files wont open on my system

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438709761438:dw dw:1438709783170:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1sorry 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

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4dw:1438709868443:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1thank you @Astrophysics , very kind.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4changing 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
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that's what the solution shows

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4you may shoot an arrow and see the starting and leaving curves to setup the bounds : dw:1438710530659:dw

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438710651083:dw When I used to do double integrals I did the same thing, it's easier to see