Consider the function f(t)=10sec^2(t)-10t^2.

Question

Consider the function f(t)=10sec^2(t)-10t^2. Let F(t) be the antiderivative of f(t) with F(0)=0.

The F(4)=______?

Answer 1

F(t) = ∫(10sec² (t) - 10t²)dt = 10tan(t)-10t³/3 + c

 

Since F(0) =0 you get c = 0

 

F(4) = 10 tan(4) - 10*4³/3