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Question: exercise 2 based on rogawskiadams 1 find the volume of...

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Exercise 2 (Based on Rogawski-Adams) (1) Find the volume of the solid object in R3 above the paraboloid surface+y2 and below 9. (2) Describe the domain of integration (also try to draw a picture R3 and compute the integral rydz dy dr.
Exercise 1 (Based on Rogawski-Adams) (1) Let f : [a, b → R be a real valued real function that is continuous on [a, b . We define F, G : [a, b as F(x) = f(t) dt and G(z) = Theorem of Calculus, show that F(r) = f(x), G,(x) = F(x) and G(x) = f(x), for all-e [a,b] f(s) ds dt for al E a, bUsing the Fundamental (2) Let us fix o E (a, b). Show (also geometrically, with a picture) that G(xo) is nothing else, but the double integral of f on a triangle in R2. By changing carefully the order of integration, also show that G(xo)o-s)f(s) ds
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