Thread: double integral

hi. could someone help me with this double integral. keep getting confused.

Double Integral: -sin(y)/(x+1)^2 + cos(x)/(y+1)^2 dydx
dy is evaluated from e(x) to x+2
dx is evaluated from 0 to 1.1462

to start with i integrated this equation with respect to y to give

Integral: [ 1/(x+1)^2cos(y) - cos(x)/y+1] dx
is this correct so far. where do i go from here
thanks

Originally Posted by mesterpa

hi. could someone help me with this double integral. keep getting confused.

Double Integral: -sin(y)/(x+1)^2 + cos(x)/(y+1)^2 dydx
dy is evaluated from e(x) to x+2
dx is evaluated from 0 to 1.1462

to start with i integrated this equation with respect to y to give

Integral: [ 1/(x+1)^2cos(y) - cos(x)/y+1] dx
is this correct so far. where do i go from here
thanks

yes, you are right so far. Now the next step is to evaluate the integral with the limits of integration. so plug in x+2 in the place of y and subtract the same function when e^x is plugged in in place of y. Then integrate the new expression with respect to x

was the lower limit x or e^x? the problem would work out more nicely if it were x and x+2

so this would give

Integral from 0 to 1.1462:

[1/(x+1)^2cos(x+2)-cos(x)/x+3] - [1/(x+1)^2cos(e(x)) - cos(x)/e(x)+1] dx

can anyone of this simplify or can i just integrate each part with respect to x

Originally Posted by mesterpa

so this would give

Integral from 0 to 1.1462:

[1/(x+1)^2cos(x+2)-cos(x)/x+3] - [1/(x+1)^2cos(e(x)) - cos(x)/e(x)+1] dx

can anyone of this simplify or can i just integrate each part with respect to x

well we can put 1/(x+1)^2cos(x+2) and 1/(x+1)^2cos(e(x)) over the same denominator, but i dont think that will make life easier. try doing it piece by piece

Originally Posted by Jhevon

was the lower limit x or e^x? the problem would work out more nicely if it were x and x+2

no its definitely e(x).
im getting really stuck here trying to integrate with respect to x. tried using matlab but im getting error messages when trying to integrate.
any help?
thanks

Originally Posted by mesterpa

no its definitely e(x).
im getting really stuck here trying to integrate with respect to x. tried using matlab but im getting error messages when trying to integrate.
any help?
thanks

I see your problem, i'm having trouble integrating some of them as well. we shall wait for a better mathematician to arrive