# Volume of Solid of Revolution Obtained by Revolving the Region Questions

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MATH120 Quiz 7 August 13, 2021 Carefully show all your work. Justify all the steps in your answer with a sentence. Answers should be exact and in simplest form unless stated otherwise. 1. (2 points) Find the area surrounded by y = e2x − ex+1 and y = ex − e. d 2. (2 points) Find dx Z x3 x2 dp t2 + 1 dt. dt 3. Determine whether the given statements are true and justify your answer. No point will be given to unjustified answer. A. (1 point) If y = f (x) is a continuous and decreasing function on [a, b], then [f (a0 ) + f (a1 ) + f (a2 ) + f (a3 ) + f (a4 ) + f (a5 ) + f (a6 )]∆x is the largest Riemann sum on the partition {a0 , a1 , a2 , a3 , a4 , a5 , a6 , a7 } where ∆x = b−a 7 and ai = a + i · ∆x for i = 0, 1, · · · , 7. B. (1 point) If y = f (x) is continuous and concave down on [a, b], the average of f on [a, b] is less than the

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