8. Definite Integrals

Evaluate the line integral of the function $f(x,y)=xy$ along the curve $C$, where $C$ is given by the parametric equations $x=t^2$, $y=2t$ for $0\le t\le 5$. That is, compute ${\int }_C^{}xyds$.

Evaluate the iterated integral: ${\int }_0^2{\int }_0^1{\left(x+y\right)}^{2}dxdy$

Evaluate the definite integral: ${\int }_1^4(t^3-t^2-4) dt$.

Find the area of the part of the plane $5x+4y+z=20$ that lies in the first octant.