Consider the function

Question

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

Then F(4)=_____?

Answer 1

F(t) = ∫f(t)dt

 

F(t) = 10∫sec²(t)dt - 10∫t²dt

 

F(t) = 10tan(t) - (10/3)t³ + C

 

 

Solve for C.

 

0 = 10tan(0) - (10/3)(0)³ + C

 

0 = C

 

Then,

 

F(4) = 10tan(4) - (10/3)(4)

       = 10tan(4) - (40/3)