Let V be the vector space of functions which are linear combinations of

1, cos x, sin x, cos 2x, sin 2x, . . . , cos(N x), sin(N x).

Let φ : V → V be the linear map

φ(f ) =∫ f (u) du. between x and 0

Calculate det φ.

I am not sure what basis to use for V when solving this. Any help would be appreciated