[" (5) Find the area bounded by the ellipse "(x^(2))/(a^(2))+(y^(2))/(b^(2))=1" and "],[" the ordinates "x=0" and "x=ea," Where "b^(2)=a^(2)(1-e^(2))],[" and "e<1],[" (5) Find the area of the region bounded by curve "y=4x^(2)" and "],[" lines "y=1,y=4" ."],[" (6) If a unit vector "vec a" makes angles "(pi)/(3)" with "hat i,(pi)/(4)" with "hat j" and the "],[" the acute angle "theta" with "hat k," then find "theta" and hence find the "],[" components of "vec a.]