Calculus Problem

Question

Find f(x) if f'(x) = 4/√1-x^2 with initial condition f(1/2) = -10 (1-x^2 is all under the square root)

Answer 1

f(x) = ∫4/√(1 - x²)dx = 4sin^-1(x) + C

f(1/2) = 4(π/6) + C = - 10. C = - 10 - 2π/3

f(x) = 4sin^-1(x) - 10 - 2π/3