Solution
= Solution
Parameterize the <straight line> by $\mathbf r(t)=(t,t,t)^T$, $0\leq t\leq1$. Then $\mathbf r'=(1,1,1)^T$ and the <line integral> becomes
$$
\int_0^1\left[2t^2+(\mu+1)t^2+(\lambda+1)t^2\right]dt
=\boxed{\frac{\lambda+\mu+4}{3}}.
$$