(1) Theorem: The area A of the region bounded by the curves y = f(x), y = g(x), and the lines x = a, x = b where f and g are continuous and f(x) ≥ g(x) for all x € [a, b] is A = Explain with an illustration. (2) Find the area of the shaded region: Y (0, 1) y = (x − 1)² (3,4) y = x + 1 X

Q: (1) Sketch the graphs y = x¹(x+2) and y = x(x+2) for the domain [-2, 1] shading the areas between…

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Q: Find the surface area generated when f(x) = sqrt(x) for 0 <= x <=1 is revolved about y = 0.

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Q: (b) A region R is bounded by the curve y=2x-4 +1 and the line 2y-x=0. (b) (i) Sketch and shade the…

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A: The region bounded by functions  , the x axis and the lines  and

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Q: (3) Sketch the graph and find its area of the region between the curves y = sinx, y = cos x over the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…