I.1.65 Double Integrals

Condition: the plate is set by the curves limiting it: \ (x = 1, \ quad y = 0, \ quad y^{2} = 4 x \ quad (y \ geq 0) \). The surface density of the plate material \ (\ mu = 7 x^{2}+y \). Find a mass of plate.

Double and itieded integrals over Various Areas of Integration, Conversion from Cartesian to Polar Coordinates, Calculation of the Jacobian, Changing the Integration, Transformation of Variables in the Integral.