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Unformatted text preview: Jake Sieger Section SEC 2 0868 Homework Set Homework3 due 10/19/2011 at 11:55pm EDT This set covers sections 6.16.3 of the text. You may need to give 4 or 5 significant digits for some (floating point) numerical answers in order to have them accepted by the computer. 1. (1 pt) The area A of the region D bounded by graphs y = 3 x 2 + 3 , y = 3 x , x = 3 , and x = 1 can be computed as an integral 1 3 x 6 y J J J J J J J J J J J J J J J J J y = 3 x 2 + 3 y = 3 x D R b a f ( x ) dx , where a = b = f ( x ) = The area A = 2. (1 pt) The area A of the region D bounded by graphs y = 1 2 x 2 , and y = 2 x 11 can be computed as an integral x 6 y A A A A A A A A A A A A A A A y = 1 2 x 2 y = 2 x 11 D R b a f ( x ) dx , where a = b = f ( x ) = The area A = 3. (1 pt) Note: You can get full credit for this prob lem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get par tial credit. The integral R 4 1 9 x 2 x 3 18 x dx MUST be evalu ated by breaking it up into a sum of three integrals: Z a 1 9 x 2 x 3 18 x dx + Z c a 9 x 2 x 3 18 x dx + Z 4 c 9 x 2 x 3 18 x dx where a = c = R a 1 9 x 2 x 3 18 x dx = R c a 9 x 2 x 3 18 x dx = R 4 c 9 x 2 x 3 18 x dx = Thus R 4 1 9 x 2 x 3 18 x dx = 4. (1 pt) Find a positive real number b such that Z 2  8cos ( x )+ b sin ( x )  dx = 36 To solve this problem, we first rewrite the expression 8cos ( x )+ b sin ( x ) in the form A sin ( x + ) where A = (your answer should be a function of b ) and is some angle between 0 and 2 . Using the trig identity sin ( + 2 ) = sin ( ) we then find that R 2  A sin ( x + )  dx = (again your answer should be a function of b ). Using the given value of the integral and solving we find that b = 1 5. (1 pt) Find the area between the curves: y = x 3 15 x 2 + 50 x and y = x 3 + 15 x 2 50 x 6. (1 pt) Note: You can get full credit for this prob lem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get par tial credit....
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 Spring '07
 Wyzlouzil

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