f(t)=4sec^2(t)-8t^2. let F(t) be antiderivative of f(t) with F(0)=0. Then F(2)=?

Answer 1

1)F(t) = int { f(t) }

= int { 4sec^2(t) - 8t^2 } dt

= 4tan(t) - (8t^3)/3 + C

2)F(0) = 0

0 = 4tan(0) - (8(0)^3)/3 + C

C = 0

so... F(t) = 4tan(t) - (8t^3)/3

3) F(2) = 4tan(2) - (8(2)^3)/3

= -8.7401 - 21.3333

= -30.0734

Answer 2

F(t) = ∫ 4 sec ² t - 8 t ² dt
F (t) = 4 tan t - (8 / 3) t ³ + C
0 = 0 - 0 + C
C = 0
F (t) = 4 tan t - (8/3) t ³
F(2) = 4 tan 2 - (8/3) (8)
F(2) = 8.74 - 64/3
F(2) = - 12.6