Find f. f '(x) = 4/ root(1 − x^2) , f (1/2) = 8

Answer 1

f(x) =∫ f ' (x) dx =4sin^-1(x) + C

Now f(1/2) = 8 => 4 * sin^-1(1/2) + C = 8

If f(x) is in radian,

C = 8 - 4 * sin^-1(1/2) = 8-2π/3

f(x) = 4 * sin^-1(1/2) + 8 -2π/3

If f(x) in degrees

=>4 *30 +C = 8 => C = -112

f(x) = 4sin^-1(x) -112 , where f(x) is in degrees