Question

I'm pretty sure the answer to this is D, but the integral doesn't come out quite right.

6. The function g(x) = 12x2 − sin x is the first derivative of f(x). If f(0) = −2, what is the value of f(2π)?

A. 30π + 2
B. 8π2 − 2
C. 4π3 + 8
D. 32π3 − 2
E. 2π2 + 5

Answer 1

integral of g(x) = 4x^3 + cos x + c = f(x)
f(0) = -2 = cos 0 + c
so c = -2-1 = -3
f(2pi) = 32pi^3 + cos(2pi) - 3
= 32pi^3 - 2

Answer 2

yup D

Answer 3

( as cos(2pi) = 1 )

Answer 4

ohhh.....that's why. I got the same thing you did for the integral. Thanks!

Answer 5

yw