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- Sketch the solid and set-up the iterated double integrals for the area of the region inside r = 3-3cosθ but outside r = 3.Consider the integral ∫17⋅x⋅cos(8⋅x) dx Which of the following choices of uu and dvdv are consistent with the principle of integration by parts? Choose all that apply. u=1u=1, dv=17⋅x⋅cos(8⋅x) dx u=17⋅x dxu=17⋅x dx, dv=cos(8⋅x) u=8⋅xu=8⋅x, dv=17⋅cos(x) dx u=17⋅xu=17⋅x, dv=8⋅sin(8⋅x) dx Choosing u=17⋅xu=17⋅x, calculate ∫17⋅x⋅cos(8⋅x) dx∫17⋅x⋅cos(8⋅x) dx What did you choose for dv= dx Your answer will be of the form 1/64(A⋅x⋅f(x)+B⋅g(x))+C where A,B∈Z and C is the constant of integration. What is A= B= f(x)= g(x)=Calculate the double integrals where R is the region 0 ≤ x ≤ π, 0 ≤ y ≤ x²