I was working through the Bott Tu book on algebraic topology and one of the questions (7.9) asks to find the top dimensional (de Rahm) cohomology ($H(M)$) and twisted cohomology ($H(M,L)$) for the compact, noncompact, orientable and nonorientable cases ($H$ is the regular cohomology, and $H_c$ the compactly supported cohomology). The answers I got are tabulated below \begin{array}{|c|c|c|c|c|} \hline \text{} & H^n(M) & H^n_c(M) & H^n(M,L) & H^n_c(M,L) \\ \hline \text{compact orientable} & \mathbb{R} & \mathbb{R} & \mathbb{R} & \mathbb{R} \\ \hline \text{noncompact orientable} & 0 & \mathbb{R} & 0 & \mathbb{R} \\ \hline \text{compact nonorientable} & 0 & 0 & \mathbb{R} & \mathbb{R} \\ \hline \text{noncompact nonorientable} & 0 & 0 & 0 & \mathbb{R} \\ \hline \end{array}
Is this correct, or have I made any errors?