00:01
To evaluate this integral.
00:01
We first apply substitution and here we let x equal to beta times t.
00:10
And so he is just x over beta and d t would be one over beta times dx.
00:25
And so from here we have the integral of x over beta squared times sine of x times one over beta dx.
00:40
And then simplifying we have one over beta to the third power times the integral of x squared times sine of x the x.
00:51
Now for this integral we will apply integration by parts.
00:56
In here we let u equal to x squared and dv equal to sine of x dx.
01:03
And so from here we have do you which is two xdx and the equal to negative cosine of x.
01:12
And so we have one over data to the third power this times u times v that's negative x squared co sign of x minus the integral of vd you that's negative cosine of x times two x dx.
01:32
And simplifying we have one over beta to the 3rd power times negative x squared cosine of x plus two integral of x.
01:44
Cosine of x dx.
01:47
And then for this integral will apply integration by parts.
01:52
Again in here we let u equal to x and dv equal to cosine of x dx.
01:59
And so we have do you echoes dx and v which is just sign of x...