i.1.65 Double integrals
Condition: The plate is defined by its bounding curves: \( x=1, \quad y=0, \quad y^{2}=4 x \quad(y \geq 0) \). Surface density of the plate material \( \mu=7 x^{2}+y \). Find the mass of the plate.
Double and iterated integrals over various areas of integration, conversion from Cartesian to polar coordinates, calculation of the Jacobian, changing the limits of integration, transformation of variables in the integral.