Question

Consider the function f ( t ) = 4 sec^2 ( t ) − 10 t^3 . Let F ( t ) be the antiderivative of f ( t ) with F ( 0 ) = 0 . Then F ( t ) =

Answer 1

∫ 4sec^2(t) - 10t^3 dt = 4tan(t) - 5/2 t^4 + C
since F(0) = 0, we have C=0
so,
F(t) = 4tan(t) - 5/2 t^4