- #1
davie
- 2
- 0
Homework Statement
To show that [tex]\int_{0}^ \frac{\pi}{2}\sqrt{cos\theta}sin^3(\theta) d\theta[/tex] = 8/21
The Attempt at a Solution
The above expression was simplified as
[tex]\int_{0}^ \frac{\pi}{2}\sqrt{cos\theta}sin^2(\theta) sin(\theta) d\theta[/tex]
[tex]\int_{0}^ \frac{\pi}{2}\sqrt{cos\theta}(1-cos^2(\theta)) sin\theta d\theta[/tex]
I have tried using integration by substitution method.
Let [tex]cos\theta = t^2[/tex]
or,[tex] sin\theta d\theta = 2tdt[/tex]
also changing the limits, when [tex]\theta = 0[/tex] , t becomes 1
and when [tex]\theta = \frac{\pi}{2} [/tex], t becomes 0
therefore the expression will look like this.
[tex]\int_{1}^ 0 t.(t^4-1)2t.dt[/tex]
Am I going into the right direction or should I use any other method like integration by parts.