F(x) = Integral of cos(x^2) dx and F(2) = 10. Find F(3).?

The answer is D as

int cos(x^2) dx =

sqrt(pi/2) C(sqrt(2/pi) x) + K

F(x = 2) = sqrt(pi/2) C(sqrt(2/pi) x) + K = 10

sqrt(pi/2) C(sqrt(2/pi) 2) + K = 10

K = 1/2 (20-sqrt(2 pi) C(2 sqrt(2/pi)))

sqrt(pi/2) C(sqrt(2/pi) x) + 1/2 (20-sqrt(2 pi) C(2 sqrt(2/pi)))

F(3)

sqrt(pi/2) C(sqrt(2/pi) 3) + 1/2 (20-sqrt(2 pi) C(2 sqrt(2/pi)))

which is about 10.241

F(x) = ∫ cos x² dx
F(x) = (1/2) sin x² + C
to find C use the given point
x=2 and F(x) = 10
Using x in radians
10 = (1/2) sin (2)² + C
C =10 - 0.5(-0.7568) = 10.3784
F(3) = (1/2) (sin 9) + 10.3784 = 0.206 + 10.3784 = 10.5844
this answer is closest to answer D.

for detailed integration steps, look here
http://www.symbolab.com/solver/step_by_s...