What Value of b Solves 1/2b^2 = sin(b)?

[Coriolis314]

This is not homework. I ran across this question in a book store a few minutes ago and can't seem to finish it...

R= int(x,0,b
S=int(cos(x),0,b
for what value of b (a positive constant) does R=S?

1/2x^2,0,b=1/2b^2
sin(x),0,b=sin(b)

1/2b^2=sin(b)

Its been a while.. but I should be able to do this... thanks

 

[Mark44]

The integrals are easy enough, but I don't think the equation you ended with has an elementary solution. One approach would be to use numeric techniquest to get an approximate solution. Another approach might be the Lambert W function.

 

[Coriolis314]

Thank you! I assumed it had a smaller function because it was in a very low level book. I think it is mean to be entered into a calculator at the last point or be cycled through an approximation algorithm.