Im stuck on this double integral, i cant see how it can be done!
Outer limit 0 - pi/2 inner limit x - pi/2
siny/y dydx
also this one
Outer limit 0 - 1 inner limit e^y - e
x/lnx dxdy
thanks
Im stuck on this double integral, i cant see how it can be done!
Outer limit 0 - pi/2 inner limit x - pi/2
siny/y dydx
also this one
Outer limit 0 - 1 inner limit e^y - e
x/lnx dxdy
thanks
Hi
$\displaystyle
\int_0^{\frac{\pi}{2}} \int_x^{\frac{\pi}{2}} y\cdot \sin y \, \mathrm{d}x \mathrm{d}y$ and $\displaystyle \int_0^1 \int_{\exp y}^{\exp 1} x\cdot \ln x \, \mathrm{d}x\mathrm{d}y $
Are these the right integrals ?
In both cases, you can first compute the inner integral...
$\displaystyle \int_0^{\frac{\pi}{2}} \int_x^{\frac{\pi}{2}} y\cdot \sin y \, \mathrm{d}x\mathrm{d}y= \int_0^{\frac{\pi}{2}} \int_x^{\frac{\pi}{2}} y\cdot \sin y \, \mathrm{d}y\mathrm{d}x=\int_0^{\frac{\pi}{2}}\left[\int_x^{\frac{\pi}{2}} y\cdot \sin y \, \mathrm{d}y\right]\mathrm{d}x$
Can you take it from here ?
No, there is no need to do this : reversing integration order brings simplifications.then should i use substitution to solve the integral?
$\displaystyle \int_0^{\frac{\pi}{2}}\int_x^{\frac{\pi}{2}}\frac{ \sin y}{y}\,\mathrm{d}x\mathrm{d}y=\int_0^{\frac{\pi}{2 }}\left[\int_0^y\frac{\sin y}{y}\,\mathrm{d}x\right]\mathrm{d}y=\int_0^{\frac{\pi}{2}}\left[\frac{\sin y}{y}\int_0^y\,\mathrm{d}x\right]\mathrm{d}y=\ldots$