# Multiple integrals help

• October 28th 2009, 09:17 AM
Multiple integrals help
1) The integral (between 4 and 1) of the integral (between 2 and 1) (x/y+y/x)dydx
2)The integral (between pi/3 and 0) of the integral (between pi/6 and 0)
xsin(x+y)dydx

Thanks!
• October 28th 2009, 09:38 AM
tonio
Quote:

1) The integral (between 4 and 1) of the integral (between 2 and 1) (x/y+y/x)dydx
2)The integral (between pi/3 and 0) of the integral (between pi/6 and 0)
xsin(x+y)dydx

Thanks!

1.- $\int\limits_1^4\int\limits_1^2 \frac{x}{y}+\frac{y}{x}\;dy\,dx=\int\limits_1^4dx\ left(\int\limits_1^2\left(\frac{x}{y}+\frac{y}{x}\ right)dy\right)=\int\limits_1^4dx\left(x\ln y+\frac{1}{2x}y^2\right)_1^2$

Well, I did the first one now you do the second one AFTER plugging in the limits (for y!) in the primitive function we got above. You get two nice, not hard integrals in x.

Try to walk now your way with problem 2 and if you get stuck somewhere in the way write back AFTER you do some work on it.

Tonio
• October 28th 2009, 12:21 PM
Quote:

Originally Posted by tonio
1.- $\int\limits_1^4\int\limits_1^2 \frac{x}{y}+\frac{y}{x}\;dy\,dx=\int\limits_1^4dx\ left(\int\limits_1^2\left(\frac{x}{y}+\frac{y}{x}\ right)dy\right)=\int\limits_1^4dx\left(x\ln y+\frac{1}{2x}y^2\right)_1^2$

Well, I did the first one now you do the second one AFTER plugging in the limits (for y!) in the primitive function we got above. You get two nice, not hard integrals in x.

Try to walk now your way with problem 2 and if you get stuck somewhere in the way write back AFTER you do some work on it.

Tonio

ok got 1 now...almost got 2, I am having trouble with a +- sign somewhere...

so for 2 I got [-xcos(x+pi/3)]-[-xcos(x)] (after I evaluated the first integral between pi/3 and 0)

integrate it becomes [-xsin(x+pi/3)+cos(x+pi/3)+cos(x)+xsin(x)]
evaluate it between pi/6 and 0 I get (-pi/12)+0.5[sqrt(3)-3], but the correct answer is (-pi/12)+0.5[sqrt(3)-1]