Tick the correct boxes. i. In variable changes of plane and space integrals, the local magnification ratio of the area or volume is always the same as the Jacobian determinant of the transformation. ii. In the variable change of the plane integral, the magnification ratio of the area is constant (i.e. does not depend on the examined point), if the variable change is linear, i.e. x=au+bv, y=cu+dv, when a,b,c,d∈R are constant. iii. In the spherical coordinate system, dV=r2sinφdrdφdθ . iv. In the spherical coordinate system, dV=drdS , when dS is interpreted as a surface element on the surface of a sphere of radius r. v. In the cylindrical coordinate system, dV=r⊥dr⊥dθdz

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A: Solution is uploaded below