If f ' (x) = 24x^2 + 6sec(x)tan(x) and f(0) = 3 then what is f(pi) = ?
If f ' (x) = 24x^2 + 6sec(x)tan(x), then
f(x) = 8x^3 + 6sec(x) + C
And
f(0)= 3 ....so
f(0) = 8(0)^3 + 6sec(0) + C = 3
6 + C = 3
Then C = -3
So
f(pi) =
8(pi)^3 + 6sec(pi) - 3 =
8(pi)^3 - 6 - 3
8(pi)^3 - 9 = about 245.05
Nice work Chris, I had to think for a bit about that first integral, it is not one that I have memorized :/