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Please show the steps in solving process. Parts of the questions are given below to give a quick idea about them; please refer to the attachment for complete and all the questions.

(1) Evaluate the line integral.

(2) Let C be a circle of radius 1 centered at the point (x,y) = (1,0). Consider the vector field F(x,y) = xi + x(1 + y)j. Calculate the two line integrals over C.

(3) Evaluate the given line integral, where C is the boundary of the region in the x-y plane enclosed by the parabola y = x^2
and the line y = 1, traversed in an anticlockwise direction.

(4) Find the area of the part of paraboloid y = x^2+z^2 that lies inside the cylinder x^2+z^2 = 1.

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The expert evaluates the given line integral.

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Please find the calculus solutions in the attached file.

(1) Given that

(2) Given that Let C be a circle of radius 1 centred at the point (x; y) = (1; 0).
In terms of parametric coordinates, we get
...

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