Solution
= Solution
With $\mathbf r(t)=(t,t^2)^T$, the <tangent vector> is $(1,2t)^T$ and $\mathbf F(\mathbf r(t))=(t^3,2t^2)^T$. The <line integral> is
$$
\int_0^1(t^3+4t^3)\,dt=\boxed{\frac54}.
$$
= Solution
With $\mathbf r(t)=(t,t^2)^T$, the <tangent vector> is $(1,2t)^T$ and $\mathbf F(\mathbf r(t))=(t^3,2t^2)^T$. The <line integral> is
$$
\int_0^1(t^3+4t^3)\,dt=\boxed{\frac54}.
$$