Integrate 1 / sqrt(25 - 16x^2) dx

The main formula is integr U^p  du  = (1/1+p)U^p+1
let be U=(25 - 16x^2)^-1/2,
1/sqrt(25 - 16x^2) = (25 - 16x^2)^-1/2
du= -1/2)(-32x)(25 - 16x^2)^-1/2dx
integ du/-1/2)(-32x)= integ(25 - 16x^2)^-1/2dx
nteg du/16x)=1/16xu+c=integ(25 - 16x^2)^-1/2dx
finally 
integ 1 / sqrt(25 - 16x^2) dx  = 1/16xu+c= (1/16x)((25 - 16x^2)^-1/2) +c
 

Step-by-step explanation:

I'd tell her that if (and only if) her prediction is correct, the probability of getting tails is 0.5.  Actually, the probability of getting heads would be the same, 0.5.

In real life she would not necessarily get 240 tails out of 480 tosses, but the mean value of the number of tails would indeed be close to 0.5.