Evaluate the following repeated integral: [Pi/2]\int[/0][Pi/2]\int[/y]cos y sin x dx dy
Jan 10, 2011 #1 pfreemanjones 1 0 Evaluate the following repeated integral: [Pi/2]\int[/0][Pi/2]\int[/y]cos y sin x dx dy
Jan 10, 2011 #2 Apphysicist 108 0 Have you ever encountered integration by iteration? Also, you need to show your attempt at a solution.
Have you ever encountered integration by iteration? Also, you need to show your attempt at a solution.
Jan 10, 2011 #3 HallsofIvy Science Advisor Homework Helper 43,008 974 This is [tex]\int_{y=0}^{\pi/2}\int_{x= y}^{\pi/2}cos(y) sin(x)dy dx[/tex] [tex]= \int_{y= 0}^{\pi/2}cos(y)\left(\int_{x= y}^{2\pi} sin(x)dx\right)dy[/tex] Now, what is [tex]\int_{x= y}^{\pi/2} sin(x)dx[/tex]?
This is [tex]\int_{y=0}^{\pi/2}\int_{x= y}^{\pi/2}cos(y) sin(x)dy dx[/tex] [tex]= \int_{y= 0}^{\pi/2}cos(y)\left(\int_{x= y}^{2\pi} sin(x)dx\right)dy[/tex] Now, what is [tex]\int_{x= y}^{\pi/2} sin(x)dx[/tex]?