Integrating Inverse Trig Functions

[Bin222]

Find f(x) if f'(x)=4/sqrt(1-x^2) and f(1/2)=1
So far I have integrated f'(x) and have found: f(x) =4arcsin(x) y=4arcsin(x) x=4sin(y)
1/2=4sin(1) 1/2=4(pi/2) 1/2=2pi
So is f(x)=1/2 or 2pi?
Thanks

 

[Deleted member 4993]

Find f(x) if f'(x)=4/sqrt(1-x^2) and f(1/2)=1
So far I have integrated f'(x) and have found:

f(x) =4arcsin(x) + C

y=4arcsin(x)

x=4sin(y)

1/2=4sin(1)

1/2=4(pi/2) ← where did π come from?

1/2=2pi
So is f(x)=1/2 or 2pi? ← none of those two - where did 'x' go?
Thanks

f(x) =4arcsin(x) + C

1 = 4 * arcsin(1/2) + C

We know → arcsin(1/2) = 2nπ + π/6

Now solve for C and finish it....

 

[Steven G]

Subhotosh,
Thank you so much for separating this for me as I was getting dizzy seeing all those equal signs.