Find the center of mass of the region R = {(x,y): 0x 1,0 y ...

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Find the center of mass of the region R = {(x,y): 0≤x≤ 1,0 ≤ y ≤ x²}, with density 6(x,y) = x+y. [5 Marks] (b) Find the half-range Fourier cosine series for the function f(x) = cosx in the range 0 ≤ x ≤ T. [5 Marks] (c) Find the equation of the tangent plane to the given surface at the point P. x² + y² + z² = 9, P(0,0,3). [5 Marks] (d) Evaluate f (x² + y²)dx + 2xydy for the curve C: x = cost, y = sint,0 ≤ t ≤ 2. C [5 Marks] Find the center of mass of the region R = {(x,y): 0≤x≤ 1,0 ≤ y ≤ x²}, with density 6(x,y) = x+y. [5 Marks] (b) Find the half-range Fourier cosine series for the function f(x) = cosx in the range 0 ≤ x ≤ T. [5 Marks] (c) Find the equation of the tangent plane to the given surface at the point P. x² + y² + z² = 9, P(0,0,3). [5 Marks] (d) Evaluate f (x² + y²)dx + 2xydy for the curve C: x = cost, y = sint,0 ≤ t ≤ 2. C [5 Marks]