Question #9abc1

1 Answer
Apr 22, 2017

8arcsin(x/4) + 4sin 2arcsin(x/4) + C

Explanation:

x=4sint => dx=4costdt

t = arcsin(x/4)

sqrt(16-x^2) = sqrt(16-(4sint)^2) = sqrt(16-16sin^2t) =

= sqrt(16(1-sin^2t)) = sqrt(16cos^2t) = 4cost

int sqrt(16-x^2)dx = int 4cost*4costdt = 16 int cos^2tdt =

16 int (1+cos2t)/2dt = 8[t+1/2sin2t]+C =

= 8arcsin(x/4) + 4sin 2arcsin(x/4) + C