`f'(x) = 4/sqrt(1 - x^2), f(1/2) = 1` Find `f`.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`f'(x)=4/sqrt(1-x^2)`

`f(x)=int(4/sqrt(1-x^2))dx`

`f(x)=4arcsin(x)+c_1`

Let's find constant c_1 , given f(1/2)=1

`f(1/2)=1=4arcsin(1/2)+c_1`

`1=4(pi/6)+c_1`

`c_1=1-(2pi)/3`

`:.f(x)=4arcsin(x)+1-(2pi)/3`