Mass of a body with variable density

Form appropriate integral sums and find their limits to solve the following problem: the length of a rod is $l=10$ meters; if the linear density of the rod varies according to the law $\delta =6+0.3x$ kilograms/meter, where $x$ is the distance from one of the two endpoints of the rod, find the mass of the rod.

Find the mass of a square plate of side $a$, given that the density at each point of the plate is proportional to the distance from that point to one of the square's vertices, and equals $\rho_{0}$ at the center of the square.

Compute the mass of the Earth's atmosphere, assuming that its density varies with height according to the law $\rho = \rho_{0} e^{-a h}$, where $h$ is the distance from the Earth's surface (regard the Earth as a sphere of radius $R$).