Consider the function f(t) = 2 sec^2 (t) − 10t^3 . Let F (t) be the antiderivative of f(t) with F(0) = 0 .

Question

Then F(3)=

Answer 1

f(t) = 2 sec^2 (t) − 10t^3
f(t) = 2tan (t) - 5/2 t^4 + c
F(0) = = 2tan 0 - 0 + c = 0 , so c = 0
then
F(t) = 2tan t - (5/2) t^4
F(3) = 2tan 3 - (5/2)(3^4) = 2tan3 - 405/2